Enumeration of the 9 sequences using 1 digit as an initial number Initial number Depth: 0 | 1| L1 0 0 0 0 0 0 0 0 , L1>=1 Depth: 1 | 2| 0 L1 0 0 0 0 0 0 0 , L1>=1 Depth: 2 | 4| 0 0 0 L1 0 0 0 0 0 , L1>=1 Depth: 3 | 8| 0 0 0 0 0 0 0 L1 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 3 | 8| 0 0 0 0 0 0 0 1 0 Depth: 4 | 16| 1 0 0 0 0 1 0 0 0 Depth: 5 | 23| 0 1 1 0 0 0 0 0 0 Depth: 6 | 46| 0 0 0 1 0 1 0 0 0 Depth: 7 | 29| 0 1 0 0 0 0 0 0 1 Depth: 8 | 58| 0 0 0 0 1 0 0 1 0 Depth: 9 | 16| 2 0 0 0 0 1 0 0 0 Depth: 10 | 23| 0 2 1 0 0 0 0 0 0 Depth: 11 | 46| 0 0 0 2 0 1 0 0 0 Depth: 12 | 289| 0 1 0 0 0 0 0 1 1 Depth: 13 | 578| 0 0 0 0 1 0 1 1 0 Depth: 14 | 156| 2 0 0 0 1 1 0 0 0 Depth: 15 | 123| 1 2 1 0 0 0 0 0 0 Depth: 16 | 246| 0 1 0 2 0 1 0 0 0 Depth: 17 | 2489| 0 1 0 1 0 0 0 1 1 Depth: 18 | 4789| 0 0 0 1 0 0 1 1 1 Depth: 19 | 5789| 0 0 0 0 1 0 1 1 1 Depth: 20 | 1578| 2 0 0 0 1 0 1 1 0 Depth: 21 | 12356| 1 1 1 0 1 1 0 0 0 Depth: 22 | 1247| 1 2 0 1 0 0 1 0 0 Depth: 23 | 249| 0 1 0 3 0 0 0 0 1 Depth: 24 | 489| 0 0 0 1 0 0 0 3 1 Depth: 25 | 789| 0 0 0 0 0 0 3 1 1 Depth: 26 | 1578| 1 0 0 0 3 0 1 1 0 Depth: 27 | 1356| 3 0 1 0 1 1 0 0 0 Depth: 28 | 127| 1 4 0 0 0 0 1 0 0 Depth: 29 | 245| 0 1 0 4 1 0 0 0 0 Depth: 30 | 489| 0 0 0 1 0 0 0 3 1 The above is the same as one at depth 24 Cyclic. length=6 inductions=0// From (d=0) | 1| 1 0 0 0 0 0 0 0 0 conditions:L1=1 (d=3). L1>=2 Depth: 4 | 167| 1 0 0 0 0 1 L1-1 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 4 | 167| 1 0 0 0 0 1 1 0 0 Depth: 5 | 34| 0 0 2 1 0 0 0 0 0 Depth: 6 | 68| 0 0 0 0 0 2 0 1 0 Depth: 7 | 136| 1 0 2 0 0 1 0 0 0 Depth: 8 | 267| 0 2 0 0 0 1 1 0 0 Depth: 9 | 345| 0 0 1 2 1 0 0 0 0 Depth: 10 | 689| 0 0 0 0 0 1 0 1 1 Depth: 11 | 1378| 1 0 1 0 0 0 1 1 0 Depth: 12 | 2567| 0 1 0 0 1 1 1 0 0 Depth: 13 | 1345| 1 0 1 1 1 0 0 0 0 Depth: 14 | 269| 0 1 0 0 0 1 0 0 1 Depth: 15 | 358| 0 0 1 0 1 0 0 1 0 Depth: 16 | 167| 1 0 0 0 0 1 1 0 0 The above is the same as one at depth 4 Cyclic. length=12 inductions=0// From (d=0) | 1| 2 0 0 0 0 0 0 0 0 conditions:L1>=2 (d=3),L1=2 (d=4). L1>=3 Depth: 5 | 345| 0 0 2 1 L1-2 0 0 0 0 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 5 | 345| 0 0 2 1 1 0 0 0 0 Depth: 6 | 69| 0 0 0 0 0 2 0 0 1 Depth: 7 | 138| 1 0 2 0 0 0 0 1 0 Depth: 8 | 267| 0 1 0 0 0 2 1 0 0 Depth: 9 | 345| 0 0 2 1 1 0 0 0 0 The above is the same as one at depth 5 Cyclic. length=4 inductions=0// From (d=0) | 1| 3 0 0 0 0 0 0 0 0 conditions:L1>=2 (d=3),L1>=3 (d=4),L1=3 (d=5). L1>=4 Depth: 6 | 169|L1-3 0 0 0 0 2 0 0 1 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 6 | 169| 1 0 0 0 0 2 0 0 1 Depth: 7 | 38| 0 0 3 0 0 0 0 1 0 Depth: 8 | 67| 0 0 0 0 0 3 1 0 0 Depth: 9 | 134| 1 0 3 1 0 0 0 0 0 Depth: 10 | 268| 0 1 0 0 0 3 0 1 0 Depth: 11 | 356| 0 0 3 0 1 1 0 0 0 Depth: 12 | 1267| 1 1 0 0 0 2 1 0 0 Depth: 13 | 2345| 0 1 2 1 1 0 0 0 0 Depth: 14 | 469| 0 0 0 1 0 2 0 0 1 Depth: 15 | 389| 0 0 2 0 0 0 0 1 1 Depth: 16 | 678| 0 0 0 0 0 1 2 1 0 Depth: 17 | 1356| 1 0 1 0 2 1 0 0 0 Depth: 18 | 127| 2 2 0 0 0 0 1 0 0 Depth: 19 | 245| 0 2 0 2 1 0 0 0 0 Depth: 20 | 489| 0 0 0 2 0 0 0 1 1 Depth: 21 | 789| 0 0 0 0 0 0 1 2 1 Depth: 22 | 1578| 1 0 0 0 1 0 2 1 0 Depth: 23 | 1356| 1 0 1 0 2 1 0 0 0 The above is the same as one at depth 17 Cyclic. length=6 inductions=0// From (d=0) | 1| 4 0 0 0 0 0 0 0 0 conditions:L1>=2 (d=3),L1>=3 (d=4),L1>=4 (d=5),L1=4 (d=6). L1>=5 Depth: 7 | 238| 0 L1-4 3 0 0 0 0 1 0 , L1>=5 Depth: 8 | 467| 0 0 0 L1-4 0 3 1 0 0 , L1>=5 Branch: L1=5(fix) or >=6 L1=5 Depth: 8 | 467| 0 0 0 1 0 3 1 0 0 Depth: 9 | 349| 0 0 3 1 0 0 0 0 1 Depth: 10 | 689| 0 0 0 0 0 3 0 1 1 Depth: 11 | 1378| 1 0 3 0 0 0 1 1 0 Depth: 12 | 2567| 0 1 0 0 1 3 1 0 0 Depth: 13 | 1345| 1 0 3 1 1 0 0 0 0 Depth: 14 | 269| 0 1 0 0 0 3 0 0 1 Depth: 15 | 358| 0 0 3 0 1 0 0 1 0 Depth: 16 | 167| 1 0 0 0 0 3 1 0 0 Depth: 17 | 34| 0 0 4 1 0 0 0 0 0 Depth: 18 | 68| 0 0 0 0 0 4 0 1 0 Depth: 19 | 136| 1 0 4 0 0 1 0 0 0 Depth: 20 | 267| 0 2 0 0 0 3 1 0 0 Depth: 21 | 345| 0 0 3 2 1 0 0 0 0 Depth: 22 | 689| 0 0 0 0 0 3 0 1 1 The above is the same as one at depth 10 Cyclic. length=12 inductions=0// From (d=0) | 1| 5 0 0 0 0 0 0 0 0 conditions:L1>=2 (d=3),L1>=3 (d=4),L1>=4 (d=5),L1>=5 (d=6),L1=5 (d=8). L1>=6 Depth: 9 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 Depth: 10 | 6789| 0 0 0 0 0 3 L1-5 1 1 , L1>=6 Depth: 11 | 13578| 1 0 3 0 L1-5 0 1 1 0 , L1>=6 Depth: 12 | 12567|L1-5 1 0 0 1 3 1 0 0 , L1>=6 Depth: 13 | 12345| 1 L1-5 3 1 1 0 0 0 0 , L1>=6 Depth: 14 | 2469| 0 1 0 L1-5 0 3 0 0 1 , L1>=6 Depth: 15 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 The above is the same as one at depth 9 Cyclic. length=6 inductions=0// From (d=0) | 1| L1 0 0 0 0 0 0 0 0 , L1>=6 conditions:L1>=2 (d=3),L1>=3 (d=4),L1>=4 (d=5),L1>=5 (d=6),L1>=6 (d=8). Initial number Depth: 0 | 2| 0 L1 0 0 0 0 0 0 0 , L1>=1 Depth: 1 | 4| 0 0 0 L1 0 0 0 0 0 , L1>=1 Depth: 2 | 8| 0 0 0 0 0 0 0 L1 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 2 | 8| 0 0 0 0 0 0 0 1 0 Depth: 3 | 16| 1 0 0 0 0 1 0 0 0 Depth: 4 | 23| 0 1 1 0 0 0 0 0 0 Depth: 5 | 46| 0 0 0 1 0 1 0 0 0 Depth: 6 | 29| 0 1 0 0 0 0 0 0 1 Depth: 7 | 58| 0 0 0 0 1 0 0 1 0 Depth: 8 | 16| 2 0 0 0 0 1 0 0 0 Depth: 9 | 23| 0 2 1 0 0 0 0 0 0 Depth: 10 | 46| 0 0 0 2 0 1 0 0 0 Depth: 11 | 289| 0 1 0 0 0 0 0 1 1 Depth: 12 | 578| 0 0 0 0 1 0 1 1 0 Depth: 13 | 156| 2 0 0 0 1 1 0 0 0 Depth: 14 | 123| 1 2 1 0 0 0 0 0 0 Depth: 15 | 246| 0 1 0 2 0 1 0 0 0 Depth: 16 | 2489| 0 1 0 1 0 0 0 1 1 Depth: 17 | 4789| 0 0 0 1 0 0 1 1 1 Depth: 18 | 5789| 0 0 0 0 1 0 1 1 1 Depth: 19 | 1578| 2 0 0 0 1 0 1 1 0 Depth: 20 | 12356| 1 1 1 0 1 1 0 0 0 Depth: 21 | 1247| 1 2 0 1 0 0 1 0 0 Depth: 22 | 249| 0 1 0 3 0 0 0 0 1 Depth: 23 | 489| 0 0 0 1 0 0 0 3 1 Depth: 24 | 789| 0 0 0 0 0 0 3 1 1 Depth: 25 | 1578| 1 0 0 0 3 0 1 1 0 Depth: 26 | 1356| 3 0 1 0 1 1 0 0 0 Depth: 27 | 127| 1 4 0 0 0 0 1 0 0 Depth: 28 | 245| 0 1 0 4 1 0 0 0 0 Depth: 29 | 489| 0 0 0 1 0 0 0 3 1 The above is the same as one at depth 23 Cyclic. length=6 inductions=0// From (d=0) | 2| 0 1 0 0 0 0 0 0 0 conditions:L1=1 (d=2). L1>=2 Depth: 3 | 167| 1 0 0 0 0 1 L1-1 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 3 | 167| 1 0 0 0 0 1 1 0 0 Depth: 4 | 34| 0 0 2 1 0 0 0 0 0 Depth: 5 | 68| 0 0 0 0 0 2 0 1 0 Depth: 6 | 136| 1 0 2 0 0 1 0 0 0 Depth: 7 | 267| 0 2 0 0 0 1 1 0 0 Depth: 8 | 345| 0 0 1 2 1 0 0 0 0 Depth: 9 | 689| 0 0 0 0 0 1 0 1 1 Depth: 10 | 1378| 1 0 1 0 0 0 1 1 0 Depth: 11 | 2567| 0 1 0 0 1 1 1 0 0 Depth: 12 | 1345| 1 0 1 1 1 0 0 0 0 Depth: 13 | 269| 0 1 0 0 0 1 0 0 1 Depth: 14 | 358| 0 0 1 0 1 0 0 1 0 Depth: 15 | 167| 1 0 0 0 0 1 1 0 0 The above is the same as one at depth 3 Cyclic. length=12 inductions=0// From (d=0) | 2| 0 2 0 0 0 0 0 0 0 conditions:L1>=2 (d=2),L1=2 (d=3). L1>=3 Depth: 4 | 345| 0 0 2 1 L1-2 0 0 0 0 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 4 | 345| 0 0 2 1 1 0 0 0 0 Depth: 5 | 69| 0 0 0 0 0 2 0 0 1 Depth: 6 | 138| 1 0 2 0 0 0 0 1 0 Depth: 7 | 267| 0 1 0 0 0 2 1 0 0 Depth: 8 | 345| 0 0 2 1 1 0 0 0 0 The above is the same as one at depth 4 Cyclic. length=4 inductions=0// From (d=0) | 2| 0 3 0 0 0 0 0 0 0 conditions:L1>=2 (d=2),L1>=3 (d=3),L1=3 (d=4). L1>=4 Depth: 5 | 169|L1-3 0 0 0 0 2 0 0 1 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 5 | 169| 1 0 0 0 0 2 0 0 1 Depth: 6 | 38| 0 0 3 0 0 0 0 1 0 Depth: 7 | 67| 0 0 0 0 0 3 1 0 0 Depth: 8 | 134| 1 0 3 1 0 0 0 0 0 Depth: 9 | 268| 0 1 0 0 0 3 0 1 0 Depth: 10 | 356| 0 0 3 0 1 1 0 0 0 Depth: 11 | 1267| 1 1 0 0 0 2 1 0 0 Depth: 12 | 2345| 0 1 2 1 1 0 0 0 0 Depth: 13 | 469| 0 0 0 1 0 2 0 0 1 Depth: 14 | 389| 0 0 2 0 0 0 0 1 1 Depth: 15 | 678| 0 0 0 0 0 1 2 1 0 Depth: 16 | 1356| 1 0 1 0 2 1 0 0 0 Depth: 17 | 127| 2 2 0 0 0 0 1 0 0 Depth: 18 | 245| 0 2 0 2 1 0 0 0 0 Depth: 19 | 489| 0 0 0 2 0 0 0 1 1 Depth: 20 | 789| 0 0 0 0 0 0 1 2 1 Depth: 21 | 1578| 1 0 0 0 1 0 2 1 0 Depth: 22 | 1356| 1 0 1 0 2 1 0 0 0 The above is the same as one at depth 16 Cyclic. length=6 inductions=0// From (d=0) | 2| 0 4 0 0 0 0 0 0 0 conditions:L1>=2 (d=2),L1>=3 (d=3),L1>=4 (d=4),L1=4 (d=5). L1>=5 Depth: 6 | 238| 0 L1-4 3 0 0 0 0 1 0 , L1>=5 Depth: 7 | 467| 0 0 0 L1-4 0 3 1 0 0 , L1>=5 Branch: L1=5(fix) or >=6 L1=5 Depth: 7 | 467| 0 0 0 1 0 3 1 0 0 Depth: 8 | 349| 0 0 3 1 0 0 0 0 1 Depth: 9 | 689| 0 0 0 0 0 3 0 1 1 Depth: 10 | 1378| 1 0 3 0 0 0 1 1 0 Depth: 11 | 2567| 0 1 0 0 1 3 1 0 0 Depth: 12 | 1345| 1 0 3 1 1 0 0 0 0 Depth: 13 | 269| 0 1 0 0 0 3 0 0 1 Depth: 14 | 358| 0 0 3 0 1 0 0 1 0 Depth: 15 | 167| 1 0 0 0 0 3 1 0 0 Depth: 16 | 34| 0 0 4 1 0 0 0 0 0 Depth: 17 | 68| 0 0 0 0 0 4 0 1 0 Depth: 18 | 136| 1 0 4 0 0 1 0 0 0 Depth: 19 | 267| 0 2 0 0 0 3 1 0 0 Depth: 20 | 345| 0 0 3 2 1 0 0 0 0 Depth: 21 | 689| 0 0 0 0 0 3 0 1 1 The above is the same as one at depth 9 Cyclic. length=12 inductions=0// From (d=0) | 2| 0 5 0 0 0 0 0 0 0 conditions:L1>=2 (d=2),L1>=3 (d=3),L1>=4 (d=4),L1>=5 (d=5),L1=5 (d=7). L1>=6 Depth: 8 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 Depth: 9 | 6789| 0 0 0 0 0 3 L1-5 1 1 , L1>=6 Depth: 10 | 13578| 1 0 3 0 L1-5 0 1 1 0 , L1>=6 Depth: 11 | 12567|L1-5 1 0 0 1 3 1 0 0 , L1>=6 Depth: 12 | 12345| 1 L1-5 3 1 1 0 0 0 0 , L1>=6 Depth: 13 | 2469| 0 1 0 L1-5 0 3 0 0 1 , L1>=6 Depth: 14 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 The above is the same as one at depth 8 Cyclic. length=6 inductions=0// From (d=0) | 2| 0 L1 0 0 0 0 0 0 0 , L1>=6 conditions:L1>=2 (d=2),L1>=3 (d=3),L1>=4 (d=4),L1>=5 (d=5),L1>=6 (d=7). Initial number Depth: 0 | 3| 0 0 L1 0 0 0 0 0 0 , L1>=1 Depth: 1 | 6| 0 0 0 0 0 L1 0 0 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 1 | 6| 0 0 0 0 0 1 0 0 0 Depth: 2 | 12| 1 1 0 0 0 0 0 0 0 Depth: 3 | 24| 0 1 0 1 0 0 0 0 0 Depth: 4 | 48| 0 0 0 1 0 0 0 1 0 Depth: 5 | 69| 0 0 0 0 0 1 0 0 1 Depth: 6 | 138| 1 0 1 0 0 0 0 1 0 Depth: 7 | 267| 0 1 0 0 0 1 1 0 0 Depth: 8 | 345| 0 0 1 1 1 0 0 0 0 Depth: 9 | 69| 0 0 0 0 0 1 0 0 1 The above is the same as one at depth 5 Cyclic. length=4 inductions=0// From (d=0) | 3| 0 0 1 0 0 0 0 0 0 conditions:L1=1 (d=1). L1>=2 Depth: 2 | 123| 1 1 L1-1 0 0 0 0 0 0 , L1>=2 Depth: 3 | 246| 0 1 0 1 0 L1-1 0 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 3 | 246| 0 1 0 1 0 1 0 0 0 Depth: 4 | 249| 0 1 0 1 0 0 0 0 1 Depth: 5 | 489| 0 0 0 1 0 0 0 1 1 Depth: 6 | 789| 0 0 0 0 0 0 1 1 1 Depth: 7 | 1578| 1 0 0 0 1 0 1 1 0 Depth: 8 | 1356| 1 0 1 0 1 1 0 0 0 Depth: 9 | 127| 1 2 0 0 0 0 1 0 0 Depth: 10 | 245| 0 1 0 2 1 0 0 0 0 Depth: 11 | 489| 0 0 0 1 0 0 0 1 1 The above is the same as one at depth 5 Cyclic. length=6 inductions=0// From (d=0) | 3| 0 0 2 0 0 0 0 0 0 conditions:L1>=2 (d=1),L1=2 (d=3). L1>=3 Depth: 4 | 2349| 0 1 L1-2 1 0 0 0 0 1 , L1>=3 Depth: 5 | 4689| 0 0 0 1 0 L1-2 0 1 1 , L1>=3 Depth: 6 | 3789| 0 0 L1-2 0 0 0 1 1 1 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 6 | 3789| 0 0 1 0 0 0 1 1 1 Depth: 7 | 578| 0 0 0 0 1 0 2 1 0 Depth: 8 | 156| 2 0 0 0 2 1 0 0 0 Depth: 9 | 123| 2 2 1 0 0 0 0 0 0 Depth: 10 | 246| 0 2 0 2 0 1 0 0 0 Depth: 11 | 2489| 0 1 0 2 0 0 0 1 1 Depth: 12 | 4789| 0 0 0 1 0 0 1 2 1 Depth: 13 | 5789| 0 0 0 0 1 0 2 1 1 Depth: 14 | 1578| 2 0 0 0 2 0 1 1 0 Depth: 15 | 12356| 2 1 1 0 1 1 0 0 0 Depth: 16 | 1247| 1 3 0 1 0 0 1 0 0 Depth: 17 | 249| 0 1 0 4 0 0 0 0 1 Depth: 18 | 489| 0 0 0 1 0 0 0 4 1 Depth: 19 | 789| 0 0 0 0 0 0 4 1 1 Depth: 20 | 1578| 1 0 0 0 4 0 1 1 0 Depth: 21 | 1356| 4 0 1 0 1 1 0 0 0 Depth: 22 | 127| 1 5 0 0 0 0 1 0 0 Depth: 23 | 245| 0 1 0 5 1 0 0 0 0 Depth: 24 | 489| 0 0 0 1 0 0 0 4 1 The above is the same as one at depth 18 Cyclic. length=6 inductions=0// From (d=0) | 3| 0 0 3 0 0 0 0 0 0 conditions:L1>=2 (d=1),L1>=3 (d=3),L1=3 (d=6). L1>=4 Depth: 7 | 5678| 0 0 0 0 1 L1-3 2 1 0 , L1>=4 Depth: 8 | 1356| 2 0 L1-3 0 2 1 0 0 0 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 8 | 1356| 2 0 1 0 2 1 0 0 0 Depth: 9 | 127| 2 3 0 0 0 0 1 0 0 Depth: 10 | 245| 0 2 0 3 1 0 0 0 0 Depth: 11 | 489| 0 0 0 2 0 0 0 2 1 Depth: 12 | 789| 0 0 0 0 0 0 2 2 1 Depth: 13 | 1578| 1 0 0 0 2 0 2 1 0 Depth: 14 | 1356| 2 0 1 0 2 1 0 0 0 The above is the same as one at depth 8 Cyclic. length=6 inductions=0// From (d=0) | 3| 0 0 4 0 0 0 0 0 0 conditions:L1>=2 (d=1),L1>=3 (d=3),L1>=4 (d=6),L1=4 (d=8). L1>=5 Depth: 9 | 1267| 2 3 0 0 0 L1-4 1 0 0 , L1>=5 Depth: 10 | 2345| 0 2 L1-4 3 1 0 0 0 0 , L1>=5 Depth: 11 | 4689| 0 0 0 2 0 L1-4 0 2 1 , L1>=5 The above is analogous to one at depth 5 | 4689| 0 0 0 1 0 L1-2 0 1 1 , L1>=5 Inductive! length=6. Check induction: check start sequence | 4689| 0 0 0 L2 0 L1 0 L2 1 , L2>=2, L1>=3 check end sequence | 4689| 0 0 0 L2+1 0 L1-2 0 L2+1 1 , L2>=2, L1>=3 Check induction: Ok 2 pre-final induction numbers preFIN 1: step diff:3*L1-22 | 4689| 0 0 0 L1 0 3 0 L1 1 , L1>=1: L1="(L1-3)/2" preFIN 2: step diff:3*L1-25 | 4689| 0 0 0 L1 0 4 0 L1 1 , L1>=1: L1="(L1-4)/2" preFIN 1 Depth: 12 | 4689| 0 0 0 L1 0 3 0 L1 1 , L1>=1: L1="(L1-3)/2" Depth: 13 | 3789| 0 0 3 0 0 0 L1 L1 1 , L1>=1: L1="(L1-3)/2" Depth: 14 | 5678| 0 0 0 0 L1 2 L1+1 1 0 , L1>=1: L1="(L1-3)/2" Depth: 15 | 1356|L1+1 0 2 0 L1+1 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 16 | 1267|L1+1 L1+2 0 0 0 1 1 0 0 , L1>=1: L1="(L1-3)/2" Depth: 17 | 2345| 0 L1+1 1 L1+2 1 0 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 18 | 4689| 0 0 0 L1+1 0 1 0 L1+1 1 , L1>=1: L1="(L1-3)/2" Depth: 19 | 3789| 0 0 1 0 0 0 L1+1 L1+1 1 , L1>=1: L1="(L1-3)/2" Depth: 20 | 578| 0 0 0 0 L1+1 0 L1+2 1 0 , L1>=1: L1="(L1-3)/2" Depth: 21 | 156|L1+2 0 0 0 L1+2 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 22 | 123|L1+2 L1+2 1 0 0 0 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 23 | 246| 0 L1+2 0 L1+2 0 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 24 | 2489| 0 1 0 L1+2 0 0 0 L1+1 1 , L1>=1: L1="(L1-3)/2" Depth: 25 | 4789| 0 0 0 1 0 0 L1+1 L1+2 1 , L1>=1: L1="(L1-3)/2" Depth: 26 | 5789| 0 0 0 0 L1+1 0 L1+2 1 1 , L1>=1: L1="(L1-3)/2" Depth: 27 | 1578|L1+2 0 0 0 L1+2 0 1 1 0 , L1>=1: L1="(L1-3)/2" Depth: 28 | 12356|L1+2 L1+1 1 0 1 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 29 | 1247| 1 L1+3 0 L1+1 0 0 1 0 0 , L1>=1: L1="(L1-3)/2" Depth: 30 | 2489| 0 1 0 L1+4 0 0 0 L1 1 , L1>=1: L1="(L1-3)/2" The above is analogous to one at depth 24 | 2489| 0 1 0 L1+2 0 0 0 L1+1 1 , L1>=1: L1="(L1-3)/2" Inductive! length=6. Check induction: check start sequence | 2489| 0 1 0 L2 0 0 0 L1 1 , L2>=5, L1>=2: L1="(L1-3)/2" check end sequence | 2489| 0 1 0 L2+2 0 0 0 L1-1 1 , L2>=5, L1>=2: L1="(L1-3)/2" Check induction: Ok 1 pre-final induction number preFIN 1: step diff:3*L1-22 | 2489| 0 1 0 L2 0 0 0 2 1 , L2>=3: L2="(3*L1-9)/2" preFIN 1 Depth: 31 | 2489| 0 1 0 L2 0 0 0 2 1 , L2>=3: L2="(3*L1-9)/2" Depth: 32 | 4789| 0 0 0 1 0 0 2 L2 1 , L2>=3: L2="(3*L1-9)/2" Depth: 33 | 5789| 0 0 0 0 2 0 L2 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 34 | 1578| 3 0 0 0 L2 0 1 1 0 , L2>=3: L2="(3*L1-9)/2" Depth: 35 | 12356| L2 2 1 0 1 1 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 36 | 1247| 1 L2+1 0 2 0 0 1 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 37 | 2489| 0 1 0 L2+2 0 0 0 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 38 | 4789| 0 0 0 1 0 0 1 L2+2 1 , L2>=3: L2="(3*L1-9)/2" Depth: 39 | 5789| 0 0 0 0 1 0 L2+2 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 40 | 1578| 2 0 0 0 L2+2 0 1 1 0 , L2>=3: L2="(3*L1-9)/2" Depth: 41 | 12356|L2+2 1 1 0 1 1 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 42 | 1247| 1 L2+3 0 1 0 0 1 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 43 | 249| 0 1 0 L2+4 0 0 0 0 1 , L2>=3: L2="(3*L1-9)/2" Depth: 44 | 489| 0 0 0 1 0 0 0 L2+4 1 , L2>=3: L2="(3*L1-9)/2" Depth: 45 | 789| 0 0 0 0 0 0 L2+4 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 46 | 1578| 1 0 0 0 L2+4 0 1 1 0 , L2>=3: L2="(3*L1-9)/2" Depth: 47 | 1356|L2+4 0 1 0 1 1 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 48 | 127| 1 L2+5 0 0 0 0 1 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 49 | 245| 0 1 0 L2+5 1 0 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 50 | 489| 0 0 0 1 0 0 0 L2+4 1 , L2>=3: L2="(3*L1-9)/2" The above is the same as one at depth 44 Cyclic. length=6 inductions=2// Length before cyclic(vars=1): 6*L1 From (d=0) | 3| 0 0 L1 0 0 0 0 0 0 , L1>=5 conditions:L1>=2 (d=1),L1>=3 (d=3),L1>=4 (d=6),L1>=5 (d=8),(L1-3)%2=0 (d=11). preFIN 2 Depth: 12 | 4689| 0 0 0 L1 0 4 0 L1 1 , L1>=1: L1="(L1-4)/2" Depth: 13 | 3789| 0 0 4 0 0 0 L1 L1 1 , L1>=1: L1="(L1-4)/2" Depth: 14 | 5678| 0 0 0 0 L1 3 L1+1 1 0 , L1>=1: L1="(L1-4)/2" Depth: 15 | 1356|L1+1 0 3 0 L1+1 1 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 16 | 1267|L1+1 L1+2 0 0 0 2 1 0 0 , L1>=1: L1="(L1-4)/2" Depth: 17 | 2345| 0 L1+1 2 L1+2 1 0 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 18 | 4689| 0 0 0 L1+1 0 2 0 L1+1 1 , L1>=1: L1="(L1-4)/2" Depth: 19 | 3789| 0 0 2 0 0 0 L1+1 L1+1 1 , L1>=1: L1="(L1-4)/2" Depth: 20 | 5678| 0 0 0 0 L1+1 1 L1+2 1 0 , L1>=1: L1="(L1-4)/2" Depth: 21 | 1356|L1+2 0 1 0 L1+2 1 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 22 | 127|L1+2 L1+3 0 0 0 0 1 0 0 , L1>=1: L1="(L1-4)/2" Depth: 23 | 245| 0 L1+2 0 L1+3 1 0 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 24 | 489| 0 0 0 L1+2 0 0 0 L1+2 1 , L1>=1: L1="(L1-4)/2" Depth: 25 | 789| 0 0 0 0 0 0 L1+2 L1+2 1 , L1>=1: L1="(L1-4)/2" Depth: 26 | 1578| 1 0 0 0 L1+2 0 L1+2 1 0 , L1>=1: L1="(L1-4)/2" Depth: 27 | 1356|L1+2 0 1 0 L1+2 1 0 0 0 , L1>=1: L1="(L1-4)/2" The above is the same as one at depth 21 Cyclic. length=6 inductions=1// Length before cyclic(vars=1): 3*L1-4 From (d=0) | 3| 0 0 L1 0 0 0 0 0 0 , L1>=5 conditions:L1>=2 (d=1),L1>=3 (d=3),L1>=4 (d=6),L1>=5 (d=8),(L1-4)%2=0 (d=11). Initial number Depth: 0 | 4| 0 0 0 L1 0 0 0 0 0 , L1>=1 Depth: 1 | 8| 0 0 0 0 0 0 0 L1 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 1 | 8| 0 0 0 0 0 0 0 1 0 Depth: 2 | 16| 1 0 0 0 0 1 0 0 0 Depth: 3 | 23| 0 1 1 0 0 0 0 0 0 Depth: 4 | 46| 0 0 0 1 0 1 0 0 0 Depth: 5 | 29| 0 1 0 0 0 0 0 0 1 Depth: 6 | 58| 0 0 0 0 1 0 0 1 0 Depth: 7 | 16| 2 0 0 0 0 1 0 0 0 Depth: 8 | 23| 0 2 1 0 0 0 0 0 0 Depth: 9 | 46| 0 0 0 2 0 1 0 0 0 Depth: 10 | 289| 0 1 0 0 0 0 0 1 1 Depth: 11 | 578| 0 0 0 0 1 0 1 1 0 Depth: 12 | 156| 2 0 0 0 1 1 0 0 0 Depth: 13 | 123| 1 2 1 0 0 0 0 0 0 Depth: 14 | 246| 0 1 0 2 0 1 0 0 0 Depth: 15 | 2489| 0 1 0 1 0 0 0 1 1 Depth: 16 | 4789| 0 0 0 1 0 0 1 1 1 Depth: 17 | 5789| 0 0 0 0 1 0 1 1 1 Depth: 18 | 1578| 2 0 0 0 1 0 1 1 0 Depth: 19 | 12356| 1 1 1 0 1 1 0 0 0 Depth: 20 | 1247| 1 2 0 1 0 0 1 0 0 Depth: 21 | 249| 0 1 0 3 0 0 0 0 1 Depth: 22 | 489| 0 0 0 1 0 0 0 3 1 Depth: 23 | 789| 0 0 0 0 0 0 3 1 1 Depth: 24 | 1578| 1 0 0 0 3 0 1 1 0 Depth: 25 | 1356| 3 0 1 0 1 1 0 0 0 Depth: 26 | 127| 1 4 0 0 0 0 1 0 0 Depth: 27 | 245| 0 1 0 4 1 0 0 0 0 Depth: 28 | 489| 0 0 0 1 0 0 0 3 1 The above is the same as one at depth 22 Cyclic. length=6 inductions=0// From (d=0) | 4| 0 0 0 1 0 0 0 0 0 conditions:L1=1 (d=1). L1>=2 Depth: 2 | 167| 1 0 0 0 0 1 L1-1 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 2 | 167| 1 0 0 0 0 1 1 0 0 Depth: 3 | 34| 0 0 2 1 0 0 0 0 0 Depth: 4 | 68| 0 0 0 0 0 2 0 1 0 Depth: 5 | 136| 1 0 2 0 0 1 0 0 0 Depth: 6 | 267| 0 2 0 0 0 1 1 0 0 Depth: 7 | 345| 0 0 1 2 1 0 0 0 0 Depth: 8 | 689| 0 0 0 0 0 1 0 1 1 Depth: 9 | 1378| 1 0 1 0 0 0 1 1 0 Depth: 10 | 2567| 0 1 0 0 1 1 1 0 0 Depth: 11 | 1345| 1 0 1 1 1 0 0 0 0 Depth: 12 | 269| 0 1 0 0 0 1 0 0 1 Depth: 13 | 358| 0 0 1 0 1 0 0 1 0 Depth: 14 | 167| 1 0 0 0 0 1 1 0 0 The above is the same as one at depth 2 Cyclic. length=12 inductions=0// From (d=0) | 4| 0 0 0 2 0 0 0 0 0 conditions:L1>=2 (d=1),L1=2 (d=2). L1>=3 Depth: 3 | 345| 0 0 2 1 L1-2 0 0 0 0 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 3 | 345| 0 0 2 1 1 0 0 0 0 Depth: 4 | 69| 0 0 0 0 0 2 0 0 1 Depth: 5 | 138| 1 0 2 0 0 0 0 1 0 Depth: 6 | 267| 0 1 0 0 0 2 1 0 0 Depth: 7 | 345| 0 0 2 1 1 0 0 0 0 The above is the same as one at depth 3 Cyclic. length=4 inductions=0// From (d=0) | 4| 0 0 0 3 0 0 0 0 0 conditions:L1>=2 (d=1),L1>=3 (d=2),L1=3 (d=3). L1>=4 Depth: 4 | 169|L1-3 0 0 0 0 2 0 0 1 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 4 | 169| 1 0 0 0 0 2 0 0 1 Depth: 5 | 38| 0 0 3 0 0 0 0 1 0 Depth: 6 | 67| 0 0 0 0 0 3 1 0 0 Depth: 7 | 134| 1 0 3 1 0 0 0 0 0 Depth: 8 | 268| 0 1 0 0 0 3 0 1 0 Depth: 9 | 356| 0 0 3 0 1 1 0 0 0 Depth: 10 | 1267| 1 1 0 0 0 2 1 0 0 Depth: 11 | 2345| 0 1 2 1 1 0 0 0 0 Depth: 12 | 469| 0 0 0 1 0 2 0 0 1 Depth: 13 | 389| 0 0 2 0 0 0 0 1 1 Depth: 14 | 678| 0 0 0 0 0 1 2 1 0 Depth: 15 | 1356| 1 0 1 0 2 1 0 0 0 Depth: 16 | 127| 2 2 0 0 0 0 1 0 0 Depth: 17 | 245| 0 2 0 2 1 0 0 0 0 Depth: 18 | 489| 0 0 0 2 0 0 0 1 1 Depth: 19 | 789| 0 0 0 0 0 0 1 2 1 Depth: 20 | 1578| 1 0 0 0 1 0 2 1 0 Depth: 21 | 1356| 1 0 1 0 2 1 0 0 0 The above is the same as one at depth 15 Cyclic. length=6 inductions=0// From (d=0) | 4| 0 0 0 4 0 0 0 0 0 conditions:L1>=2 (d=1),L1>=3 (d=2),L1>=4 (d=3),L1=4 (d=4). L1>=5 Depth: 5 | 238| 0 L1-4 3 0 0 0 0 1 0 , L1>=5 Depth: 6 | 467| 0 0 0 L1-4 0 3 1 0 0 , L1>=5 Branch: L1=5(fix) or >=6 L1=5 Depth: 6 | 467| 0 0 0 1 0 3 1 0 0 Depth: 7 | 349| 0 0 3 1 0 0 0 0 1 Depth: 8 | 689| 0 0 0 0 0 3 0 1 1 Depth: 9 | 1378| 1 0 3 0 0 0 1 1 0 Depth: 10 | 2567| 0 1 0 0 1 3 1 0 0 Depth: 11 | 1345| 1 0 3 1 1 0 0 0 0 Depth: 12 | 269| 0 1 0 0 0 3 0 0 1 Depth: 13 | 358| 0 0 3 0 1 0 0 1 0 Depth: 14 | 167| 1 0 0 0 0 3 1 0 0 Depth: 15 | 34| 0 0 4 1 0 0 0 0 0 Depth: 16 | 68| 0 0 0 0 0 4 0 1 0 Depth: 17 | 136| 1 0 4 0 0 1 0 0 0 Depth: 18 | 267| 0 2 0 0 0 3 1 0 0 Depth: 19 | 345| 0 0 3 2 1 0 0 0 0 Depth: 20 | 689| 0 0 0 0 0 3 0 1 1 The above is the same as one at depth 8 Cyclic. length=12 inductions=0// From (d=0) | 4| 0 0 0 5 0 0 0 0 0 conditions:L1>=2 (d=1),L1>=3 (d=2),L1>=4 (d=3),L1>=5 (d=4),L1=5 (d=6). L1>=6 Depth: 7 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 Depth: 8 | 6789| 0 0 0 0 0 3 L1-5 1 1 , L1>=6 Depth: 9 | 13578| 1 0 3 0 L1-5 0 1 1 0 , L1>=6 Depth: 10 | 12567|L1-5 1 0 0 1 3 1 0 0 , L1>=6 Depth: 11 | 12345| 1 L1-5 3 1 1 0 0 0 0 , L1>=6 Depth: 12 | 2469| 0 1 0 L1-5 0 3 0 0 1 , L1>=6 Depth: 13 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 The above is the same as one at depth 7 Cyclic. length=6 inductions=0// From (d=0) | 4| 0 0 0 L1 0 0 0 0 0 , L1>=6 conditions:L1>=2 (d=1),L1>=3 (d=2),L1>=4 (d=3),L1>=5 (d=4),L1>=6 (d=6). Initial number Depth: 0 | 5| 0 0 0 0 L1 0 0 0 0 , L1>=1 Depth: 1 | 1| L1 0 0 0 0 0 0 0 0 , L1>=1 Depth: 2 | 2| 0 L1 0 0 0 0 0 0 0 , L1>=1 Depth: 3 | 4| 0 0 0 L1 0 0 0 0 0 , L1>=1 Depth: 4 | 8| 0 0 0 0 0 0 0 L1 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 4 | 8| 0 0 0 0 0 0 0 1 0 Depth: 5 | 16| 1 0 0 0 0 1 0 0 0 Depth: 6 | 23| 0 1 1 0 0 0 0 0 0 Depth: 7 | 46| 0 0 0 1 0 1 0 0 0 Depth: 8 | 29| 0 1 0 0 0 0 0 0 1 Depth: 9 | 58| 0 0 0 0 1 0 0 1 0 Depth: 10 | 16| 2 0 0 0 0 1 0 0 0 Depth: 11 | 23| 0 2 1 0 0 0 0 0 0 Depth: 12 | 46| 0 0 0 2 0 1 0 0 0 Depth: 13 | 289| 0 1 0 0 0 0 0 1 1 Depth: 14 | 578| 0 0 0 0 1 0 1 1 0 Depth: 15 | 156| 2 0 0 0 1 1 0 0 0 Depth: 16 | 123| 1 2 1 0 0 0 0 0 0 Depth: 17 | 246| 0 1 0 2 0 1 0 0 0 Depth: 18 | 2489| 0 1 0 1 0 0 0 1 1 Depth: 19 | 4789| 0 0 0 1 0 0 1 1 1 Depth: 20 | 5789| 0 0 0 0 1 0 1 1 1 Depth: 21 | 1578| 2 0 0 0 1 0 1 1 0 Depth: 22 | 12356| 1 1 1 0 1 1 0 0 0 Depth: 23 | 1247| 1 2 0 1 0 0 1 0 0 Depth: 24 | 249| 0 1 0 3 0 0 0 0 1 Depth: 25 | 489| 0 0 0 1 0 0 0 3 1 Depth: 26 | 789| 0 0 0 0 0 0 3 1 1 Depth: 27 | 1578| 1 0 0 0 3 0 1 1 0 Depth: 28 | 1356| 3 0 1 0 1 1 0 0 0 Depth: 29 | 127| 1 4 0 0 0 0 1 0 0 Depth: 30 | 245| 0 1 0 4 1 0 0 0 0 Depth: 31 | 489| 0 0 0 1 0 0 0 3 1 The above is the same as one at depth 25 Cyclic. length=6 inductions=0// From (d=0) | 5| 0 0 0 0 1 0 0 0 0 conditions:L1=1 (d=4). L1>=2 Depth: 5 | 167| 1 0 0 0 0 1 L1-1 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 5 | 167| 1 0 0 0 0 1 1 0 0 Depth: 6 | 34| 0 0 2 1 0 0 0 0 0 Depth: 7 | 68| 0 0 0 0 0 2 0 1 0 Depth: 8 | 136| 1 0 2 0 0 1 0 0 0 Depth: 9 | 267| 0 2 0 0 0 1 1 0 0 Depth: 10 | 345| 0 0 1 2 1 0 0 0 0 Depth: 11 | 689| 0 0 0 0 0 1 0 1 1 Depth: 12 | 1378| 1 0 1 0 0 0 1 1 0 Depth: 13 | 2567| 0 1 0 0 1 1 1 0 0 Depth: 14 | 1345| 1 0 1 1 1 0 0 0 0 Depth: 15 | 269| 0 1 0 0 0 1 0 0 1 Depth: 16 | 358| 0 0 1 0 1 0 0 1 0 Depth: 17 | 167| 1 0 0 0 0 1 1 0 0 The above is the same as one at depth 5 Cyclic. length=12 inductions=0// From (d=0) | 5| 0 0 0 0 2 0 0 0 0 conditions:L1>=2 (d=4),L1=2 (d=5). L1>=3 Depth: 6 | 345| 0 0 2 1 L1-2 0 0 0 0 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 6 | 345| 0 0 2 1 1 0 0 0 0 Depth: 7 | 69| 0 0 0 0 0 2 0 0 1 Depth: 8 | 138| 1 0 2 0 0 0 0 1 0 Depth: 9 | 267| 0 1 0 0 0 2 1 0 0 Depth: 10 | 345| 0 0 2 1 1 0 0 0 0 The above is the same as one at depth 6 Cyclic. length=4 inductions=0// From (d=0) | 5| 0 0 0 0 3 0 0 0 0 conditions:L1>=2 (d=4),L1>=3 (d=5),L1=3 (d=6). L1>=4 Depth: 7 | 169|L1-3 0 0 0 0 2 0 0 1 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 7 | 169| 1 0 0 0 0 2 0 0 1 Depth: 8 | 38| 0 0 3 0 0 0 0 1 0 Depth: 9 | 67| 0 0 0 0 0 3 1 0 0 Depth: 10 | 134| 1 0 3 1 0 0 0 0 0 Depth: 11 | 268| 0 1 0 0 0 3 0 1 0 Depth: 12 | 356| 0 0 3 0 1 1 0 0 0 Depth: 13 | 1267| 1 1 0 0 0 2 1 0 0 Depth: 14 | 2345| 0 1 2 1 1 0 0 0 0 Depth: 15 | 469| 0 0 0 1 0 2 0 0 1 Depth: 16 | 389| 0 0 2 0 0 0 0 1 1 Depth: 17 | 678| 0 0 0 0 0 1 2 1 0 Depth: 18 | 1356| 1 0 1 0 2 1 0 0 0 Depth: 19 | 127| 2 2 0 0 0 0 1 0 0 Depth: 20 | 245| 0 2 0 2 1 0 0 0 0 Depth: 21 | 489| 0 0 0 2 0 0 0 1 1 Depth: 22 | 789| 0 0 0 0 0 0 1 2 1 Depth: 23 | 1578| 1 0 0 0 1 0 2 1 0 Depth: 24 | 1356| 1 0 1 0 2 1 0 0 0 The above is the same as one at depth 18 Cyclic. length=6 inductions=0// From (d=0) | 5| 0 0 0 0 4 0 0 0 0 conditions:L1>=2 (d=4),L1>=3 (d=5),L1>=4 (d=6),L1=4 (d=7). L1>=5 Depth: 8 | 238| 0 L1-4 3 0 0 0 0 1 0 , L1>=5 Depth: 9 | 467| 0 0 0 L1-4 0 3 1 0 0 , L1>=5 Branch: L1=5(fix) or >=6 L1=5 Depth: 9 | 467| 0 0 0 1 0 3 1 0 0 Depth: 10 | 349| 0 0 3 1 0 0 0 0 1 Depth: 11 | 689| 0 0 0 0 0 3 0 1 1 Depth: 12 | 1378| 1 0 3 0 0 0 1 1 0 Depth: 13 | 2567| 0 1 0 0 1 3 1 0 0 Depth: 14 | 1345| 1 0 3 1 1 0 0 0 0 Depth: 15 | 269| 0 1 0 0 0 3 0 0 1 Depth: 16 | 358| 0 0 3 0 1 0 0 1 0 Depth: 17 | 167| 1 0 0 0 0 3 1 0 0 Depth: 18 | 34| 0 0 4 1 0 0 0 0 0 Depth: 19 | 68| 0 0 0 0 0 4 0 1 0 Depth: 20 | 136| 1 0 4 0 0 1 0 0 0 Depth: 21 | 267| 0 2 0 0 0 3 1 0 0 Depth: 22 | 345| 0 0 3 2 1 0 0 0 0 Depth: 23 | 689| 0 0 0 0 0 3 0 1 1 The above is the same as one at depth 11 Cyclic. length=12 inductions=0// From (d=0) | 5| 0 0 0 0 5 0 0 0 0 conditions:L1>=2 (d=4),L1>=3 (d=5),L1>=4 (d=6),L1>=5 (d=7),L1=5 (d=9). L1>=6 Depth: 10 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 Depth: 11 | 6789| 0 0 0 0 0 3 L1-5 1 1 , L1>=6 Depth: 12 | 13578| 1 0 3 0 L1-5 0 1 1 0 , L1>=6 Depth: 13 | 12567|L1-5 1 0 0 1 3 1 0 0 , L1>=6 Depth: 14 | 12345| 1 L1-5 3 1 1 0 0 0 0 , L1>=6 Depth: 15 | 2469| 0 1 0 L1-5 0 3 0 0 1 , L1>=6 Depth: 16 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 The above is the same as one at depth 10 Cyclic. length=6 inductions=0// From (d=0) | 5| 0 0 0 0 L1 0 0 0 0 , L1>=6 conditions:L1>=2 (d=4),L1>=3 (d=5),L1>=4 (d=6),L1>=5 (d=7),L1>=6 (d=9). Initial number Depth: 0 | 6| 0 0 0 0 0 L1 0 0 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 0 | 6| 0 0 0 0 0 1 0 0 0 Depth: 1 | 12| 1 1 0 0 0 0 0 0 0 Depth: 2 | 24| 0 1 0 1 0 0 0 0 0 Depth: 3 | 48| 0 0 0 1 0 0 0 1 0 Depth: 4 | 69| 0 0 0 0 0 1 0 0 1 Depth: 5 | 138| 1 0 1 0 0 0 0 1 0 Depth: 6 | 267| 0 1 0 0 0 1 1 0 0 Depth: 7 | 345| 0 0 1 1 1 0 0 0 0 Depth: 8 | 69| 0 0 0 0 0 1 0 0 1 The above is the same as one at depth 4 Cyclic. length=4 inductions=0// From (d=0) | 6| 0 0 0 0 0 1 0 0 0 conditions:L1=1 (d=0). L1>=2 Depth: 1 | 123| 1 1 L1-1 0 0 0 0 0 0 , L1>=2 Depth: 2 | 246| 0 1 0 1 0 L1-1 0 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 2 | 246| 0 1 0 1 0 1 0 0 0 Depth: 3 | 249| 0 1 0 1 0 0 0 0 1 Depth: 4 | 489| 0 0 0 1 0 0 0 1 1 Depth: 5 | 789| 0 0 0 0 0 0 1 1 1 Depth: 6 | 1578| 1 0 0 0 1 0 1 1 0 Depth: 7 | 1356| 1 0 1 0 1 1 0 0 0 Depth: 8 | 127| 1 2 0 0 0 0 1 0 0 Depth: 9 | 245| 0 1 0 2 1 0 0 0 0 Depth: 10 | 489| 0 0 0 1 0 0 0 1 1 The above is the same as one at depth 4 Cyclic. length=6 inductions=0// From (d=0) | 6| 0 0 0 0 0 2 0 0 0 conditions:L1>=2 (d=0),L1=2 (d=2). L1>=3 Depth: 3 | 2349| 0 1 L1-2 1 0 0 0 0 1 , L1>=3 Depth: 4 | 4689| 0 0 0 1 0 L1-2 0 1 1 , L1>=3 Depth: 5 | 3789| 0 0 L1-2 0 0 0 1 1 1 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 5 | 3789| 0 0 1 0 0 0 1 1 1 Depth: 6 | 578| 0 0 0 0 1 0 2 1 0 Depth: 7 | 156| 2 0 0 0 2 1 0 0 0 Depth: 8 | 123| 2 2 1 0 0 0 0 0 0 Depth: 9 | 246| 0 2 0 2 0 1 0 0 0 Depth: 10 | 2489| 0 1 0 2 0 0 0 1 1 Depth: 11 | 4789| 0 0 0 1 0 0 1 2 1 Depth: 12 | 5789| 0 0 0 0 1 0 2 1 1 Depth: 13 | 1578| 2 0 0 0 2 0 1 1 0 Depth: 14 | 12356| 2 1 1 0 1 1 0 0 0 Depth: 15 | 1247| 1 3 0 1 0 0 1 0 0 Depth: 16 | 249| 0 1 0 4 0 0 0 0 1 Depth: 17 | 489| 0 0 0 1 0 0 0 4 1 Depth: 18 | 789| 0 0 0 0 0 0 4 1 1 Depth: 19 | 1578| 1 0 0 0 4 0 1 1 0 Depth: 20 | 1356| 4 0 1 0 1 1 0 0 0 Depth: 21 | 127| 1 5 0 0 0 0 1 0 0 Depth: 22 | 245| 0 1 0 5 1 0 0 0 0 Depth: 23 | 489| 0 0 0 1 0 0 0 4 1 The above is the same as one at depth 17 Cyclic. length=6 inductions=0// From (d=0) | 6| 0 0 0 0 0 3 0 0 0 conditions:L1>=2 (d=0),L1>=3 (d=2),L1=3 (d=5). L1>=4 Depth: 6 | 5678| 0 0 0 0 1 L1-3 2 1 0 , L1>=4 Depth: 7 | 1356| 2 0 L1-3 0 2 1 0 0 0 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 7 | 1356| 2 0 1 0 2 1 0 0 0 Depth: 8 | 127| 2 3 0 0 0 0 1 0 0 Depth: 9 | 245| 0 2 0 3 1 0 0 0 0 Depth: 10 | 489| 0 0 0 2 0 0 0 2 1 Depth: 11 | 789| 0 0 0 0 0 0 2 2 1 Depth: 12 | 1578| 1 0 0 0 2 0 2 1 0 Depth: 13 | 1356| 2 0 1 0 2 1 0 0 0 The above is the same as one at depth 7 Cyclic. length=6 inductions=0// From (d=0) | 6| 0 0 0 0 0 4 0 0 0 conditions:L1>=2 (d=0),L1>=3 (d=2),L1>=4 (d=5),L1=4 (d=7). L1>=5 Depth: 8 | 1267| 2 3 0 0 0 L1-4 1 0 0 , L1>=5 Depth: 9 | 2345| 0 2 L1-4 3 1 0 0 0 0 , L1>=5 Depth: 10 | 4689| 0 0 0 2 0 L1-4 0 2 1 , L1>=5 The above is analogous to one at depth 4 | 4689| 0 0 0 1 0 L1-2 0 1 1 , L1>=5 Inductive! length=6. Check induction: check start sequence | 4689| 0 0 0 L2 0 L1 0 L2 1 , L2>=2, L1>=3 check end sequence | 4689| 0 0 0 L2+1 0 L1-2 0 L2+1 1 , L2>=2, L1>=3 Check induction: Ok 2 pre-final induction numbers preFIN 1: step diff:3*L1-22 | 4689| 0 0 0 L1 0 3 0 L1 1 , L1>=1: L1="(L1-3)/2" preFIN 2: step diff:3*L1-25 | 4689| 0 0 0 L1 0 4 0 L1 1 , L1>=1: L1="(L1-4)/2" preFIN 1 Depth: 11 | 4689| 0 0 0 L1 0 3 0 L1 1 , L1>=1: L1="(L1-3)/2" Depth: 12 | 3789| 0 0 3 0 0 0 L1 L1 1 , L1>=1: L1="(L1-3)/2" Depth: 13 | 5678| 0 0 0 0 L1 2 L1+1 1 0 , L1>=1: L1="(L1-3)/2" Depth: 14 | 1356|L1+1 0 2 0 L1+1 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 15 | 1267|L1+1 L1+2 0 0 0 1 1 0 0 , L1>=1: L1="(L1-3)/2" Depth: 16 | 2345| 0 L1+1 1 L1+2 1 0 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 17 | 4689| 0 0 0 L1+1 0 1 0 L1+1 1 , L1>=1: L1="(L1-3)/2" Depth: 18 | 3789| 0 0 1 0 0 0 L1+1 L1+1 1 , L1>=1: L1="(L1-3)/2" Depth: 19 | 578| 0 0 0 0 L1+1 0 L1+2 1 0 , L1>=1: L1="(L1-3)/2" Depth: 20 | 156|L1+2 0 0 0 L1+2 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 21 | 123|L1+2 L1+2 1 0 0 0 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 22 | 246| 0 L1+2 0 L1+2 0 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 23 | 2489| 0 1 0 L1+2 0 0 0 L1+1 1 , L1>=1: L1="(L1-3)/2" Depth: 24 | 4789| 0 0 0 1 0 0 L1+1 L1+2 1 , L1>=1: L1="(L1-3)/2" Depth: 25 | 5789| 0 0 0 0 L1+1 0 L1+2 1 1 , L1>=1: L1="(L1-3)/2" Depth: 26 | 1578|L1+2 0 0 0 L1+2 0 1 1 0 , L1>=1: L1="(L1-3)/2" Depth: 27 | 12356|L1+2 L1+1 1 0 1 1 0 0 0 , L1>=1: L1="(L1-3)/2" Depth: 28 | 1247| 1 L1+3 0 L1+1 0 0 1 0 0 , L1>=1: L1="(L1-3)/2" Depth: 29 | 2489| 0 1 0 L1+4 0 0 0 L1 1 , L1>=1: L1="(L1-3)/2" The above is analogous to one at depth 23 | 2489| 0 1 0 L1+2 0 0 0 L1+1 1 , L1>=1: L1="(L1-3)/2" Inductive! length=6. Check induction: check start sequence | 2489| 0 1 0 L2 0 0 0 L1 1 , L2>=5, L1>=2: L1="(L1-3)/2" check end sequence | 2489| 0 1 0 L2+2 0 0 0 L1-1 1 , L2>=5, L1>=2: L1="(L1-3)/2" Check induction: Ok 1 pre-final induction number preFIN 1: step diff:3*L1-22 | 2489| 0 1 0 L2 0 0 0 2 1 , L2>=3: L2="(3*L1-9)/2" preFIN 1 Depth: 30 | 2489| 0 1 0 L2 0 0 0 2 1 , L2>=3: L2="(3*L1-9)/2" Depth: 31 | 4789| 0 0 0 1 0 0 2 L2 1 , L2>=3: L2="(3*L1-9)/2" Depth: 32 | 5789| 0 0 0 0 2 0 L2 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 33 | 1578| 3 0 0 0 L2 0 1 1 0 , L2>=3: L2="(3*L1-9)/2" Depth: 34 | 12356| L2 2 1 0 1 1 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 35 | 1247| 1 L2+1 0 2 0 0 1 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 36 | 2489| 0 1 0 L2+2 0 0 0 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 37 | 4789| 0 0 0 1 0 0 1 L2+2 1 , L2>=3: L2="(3*L1-9)/2" Depth: 38 | 5789| 0 0 0 0 1 0 L2+2 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 39 | 1578| 2 0 0 0 L2+2 0 1 1 0 , L2>=3: L2="(3*L1-9)/2" Depth: 40 | 12356|L2+2 1 1 0 1 1 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 41 | 1247| 1 L2+3 0 1 0 0 1 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 42 | 249| 0 1 0 L2+4 0 0 0 0 1 , L2>=3: L2="(3*L1-9)/2" Depth: 43 | 489| 0 0 0 1 0 0 0 L2+4 1 , L2>=3: L2="(3*L1-9)/2" Depth: 44 | 789| 0 0 0 0 0 0 L2+4 1 1 , L2>=3: L2="(3*L1-9)/2" Depth: 45 | 1578| 1 0 0 0 L2+4 0 1 1 0 , L2>=3: L2="(3*L1-9)/2" Depth: 46 | 1356|L2+4 0 1 0 1 1 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 47 | 127| 1 L2+5 0 0 0 0 1 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 48 | 245| 0 1 0 L2+5 1 0 0 0 0 , L2>=3: L2="(3*L1-9)/2" Depth: 49 | 489| 0 0 0 1 0 0 0 L2+4 1 , L2>=3: L2="(3*L1-9)/2" The above is the same as one at depth 43 Cyclic. length=6 inductions=2// Length before cyclic(vars=1): 6*L1-1 From (d=0) | 6| 0 0 0 0 0 L1 0 0 0 , L1>=5 conditions:L1>=2 (d=0),L1>=3 (d=2),L1>=4 (d=5),L1>=5 (d=7),(L1-3)%2=0 (d=10). preFIN 2 Depth: 11 | 4689| 0 0 0 L1 0 4 0 L1 1 , L1>=1: L1="(L1-4)/2" Depth: 12 | 3789| 0 0 4 0 0 0 L1 L1 1 , L1>=1: L1="(L1-4)/2" Depth: 13 | 5678| 0 0 0 0 L1 3 L1+1 1 0 , L1>=1: L1="(L1-4)/2" Depth: 14 | 1356|L1+1 0 3 0 L1+1 1 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 15 | 1267|L1+1 L1+2 0 0 0 2 1 0 0 , L1>=1: L1="(L1-4)/2" Depth: 16 | 2345| 0 L1+1 2 L1+2 1 0 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 17 | 4689| 0 0 0 L1+1 0 2 0 L1+1 1 , L1>=1: L1="(L1-4)/2" Depth: 18 | 3789| 0 0 2 0 0 0 L1+1 L1+1 1 , L1>=1: L1="(L1-4)/2" Depth: 19 | 5678| 0 0 0 0 L1+1 1 L1+2 1 0 , L1>=1: L1="(L1-4)/2" Depth: 20 | 1356|L1+2 0 1 0 L1+2 1 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 21 | 127|L1+2 L1+3 0 0 0 0 1 0 0 , L1>=1: L1="(L1-4)/2" Depth: 22 | 245| 0 L1+2 0 L1+3 1 0 0 0 0 , L1>=1: L1="(L1-4)/2" Depth: 23 | 489| 0 0 0 L1+2 0 0 0 L1+2 1 , L1>=1: L1="(L1-4)/2" Depth: 24 | 789| 0 0 0 0 0 0 L1+2 L1+2 1 , L1>=1: L1="(L1-4)/2" Depth: 25 | 1578| 1 0 0 0 L1+2 0 L1+2 1 0 , L1>=1: L1="(L1-4)/2" Depth: 26 | 1356|L1+2 0 1 0 L1+2 1 0 0 0 , L1>=1: L1="(L1-4)/2" The above is the same as one at depth 20 Cyclic. length=6 inductions=1// Length before cyclic(vars=1): 3*L1-5 From (d=0) | 6| 0 0 0 0 0 L1 0 0 0 , L1>=5 conditions:L1>=2 (d=0),L1>=3 (d=2),L1>=4 (d=5),L1>=5 (d=7),(L1-4)%2=0 (d=10). Initial number Depth: 0 | 7| 0 0 0 0 0 0 L1 0 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 0 | 7| 0 0 0 0 0 0 1 0 0 Depth: 1 | 14| 1 0 0 1 0 0 0 0 0 Depth: 2 | 28| 0 1 0 0 0 0 0 1 0 Depth: 3 | 56| 0 0 0 0 1 1 0 0 0 Depth: 4 | 12| 2 1 0 0 0 0 0 0 0 Depth: 5 | 24| 0 2 0 1 0 0 0 0 0 Depth: 6 | 48| 0 0 0 2 0 0 0 1 0 Depth: 7 | 689| 0 0 0 0 0 1 0 1 1 Depth: 8 | 1378| 1 0 1 0 0 0 1 1 0 Depth: 9 | 2567| 0 1 0 0 1 1 1 0 0 Depth: 10 | 1345| 1 0 1 1 1 0 0 0 0 Depth: 11 | 269| 0 1 0 0 0 1 0 0 1 Depth: 12 | 358| 0 0 1 0 1 0 0 1 0 Depth: 13 | 167| 1 0 0 0 0 1 1 0 0 Depth: 14 | 34| 0 0 2 1 0 0 0 0 0 Depth: 15 | 68| 0 0 0 0 0 2 0 1 0 Depth: 16 | 136| 1 0 2 0 0 1 0 0 0 Depth: 17 | 267| 0 2 0 0 0 1 1 0 0 Depth: 18 | 345| 0 0 1 2 1 0 0 0 0 Depth: 19 | 689| 0 0 0 0 0 1 0 1 1 The above is the same as one at depth 7 Cyclic. length=12 inductions=0// From (d=0) | 7| 0 0 0 0 0 0 1 0 0 conditions:L1=1 (d=0). L1>=2 Depth: 1 | 145| 1 0 0 1 L1-1 0 0 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 1 | 145| 1 0 0 1 1 0 0 0 0 Depth: 2 | 29| 0 1 0 0 0 0 0 0 1 Depth: 3 | 58| 0 0 0 0 1 0 0 1 0 Depth: 4 | 16| 2 0 0 0 0 1 0 0 0 Depth: 5 | 23| 0 2 1 0 0 0 0 0 0 Depth: 6 | 46| 0 0 0 2 0 1 0 0 0 Depth: 7 | 289| 0 1 0 0 0 0 0 1 1 Depth: 8 | 578| 0 0 0 0 1 0 1 1 0 Depth: 9 | 156| 2 0 0 0 1 1 0 0 0 Depth: 10 | 123| 1 2 1 0 0 0 0 0 0 Depth: 11 | 246| 0 1 0 2 0 1 0 0 0 Depth: 12 | 2489| 0 1 0 1 0 0 0 1 1 Depth: 13 | 4789| 0 0 0 1 0 0 1 1 1 Depth: 14 | 5789| 0 0 0 0 1 0 1 1 1 Depth: 15 | 1578| 2 0 0 0 1 0 1 1 0 Depth: 16 | 12356| 1 1 1 0 1 1 0 0 0 Depth: 17 | 1247| 1 2 0 1 0 0 1 0 0 Depth: 18 | 249| 0 1 0 3 0 0 0 0 1 Depth: 19 | 489| 0 0 0 1 0 0 0 3 1 Depth: 20 | 789| 0 0 0 0 0 0 3 1 1 Depth: 21 | 1578| 1 0 0 0 3 0 1 1 0 Depth: 22 | 1356| 3 0 1 0 1 1 0 0 0 Depth: 23 | 127| 1 4 0 0 0 0 1 0 0 Depth: 24 | 245| 0 1 0 4 1 0 0 0 0 Depth: 25 | 489| 0 0 0 1 0 0 0 3 1 The above is the same as one at depth 19 Cyclic. length=6 inductions=0// From (d=0) | 7| 0 0 0 0 0 0 2 0 0 conditions:L1>=2 (d=0),L1=2 (d=1). L1>=3 Depth: 2 | 129|L1-2 1 0 0 0 0 0 0 1 , L1>=3 Depth: 3 | 258| 0 L1-2 0 0 1 0 0 1 0 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 3 | 258| 0 1 0 0 1 0 0 1 0 Depth: 4 | 156| 1 0 0 0 1 1 0 0 0 Depth: 5 | 123| 1 1 1 0 0 0 0 0 0 Depth: 6 | 246| 0 1 0 1 0 1 0 0 0 Depth: 7 | 249| 0 1 0 1 0 0 0 0 1 Depth: 8 | 489| 0 0 0 1 0 0 0 1 1 Depth: 9 | 789| 0 0 0 0 0 0 1 1 1 Depth: 10 | 1578| 1 0 0 0 1 0 1 1 0 Depth: 11 | 1356| 1 0 1 0 1 1 0 0 0 Depth: 12 | 127| 1 2 0 0 0 0 1 0 0 Depth: 13 | 245| 0 1 0 2 1 0 0 0 0 Depth: 14 | 489| 0 0 0 1 0 0 0 1 1 The above is the same as one at depth 8 Cyclic. length=6 inductions=0// From (d=0) | 7| 0 0 0 0 0 0 3 0 0 conditions:L1>=2 (d=0),L1>=3 (d=1),L1=3 (d=3). L1>=4 Depth: 4 | 1456| 1 0 0 L1-3 1 1 0 0 0 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 4 | 1456| 1 0 0 1 1 1 0 0 0 Depth: 5 | 129| 1 2 0 0 0 0 0 0 1 Depth: 6 | 2458| 0 1 0 1 1 0 0 1 0 Depth: 7 | 1469| 1 0 0 1 0 1 0 0 1 Depth: 8 | 2389| 0 1 1 0 0 0 0 1 1 Depth: 9 | 478| 0 0 0 1 0 0 2 1 0 Depth: 10 | 569| 0 0 0 0 2 1 0 0 1 Depth: 11 | 138| 3 0 1 0 0 0 0 1 0 Depth: 12 | 267| 0 3 0 0 0 1 1 0 0 Depth: 13 | 345| 0 0 1 3 1 0 0 0 0 Depth: 14 | 689| 0 0 0 0 0 1 0 2 1 Depth: 15 | 1378| 1 0 1 0 0 0 2 1 0 Depth: 16 | 2567| 0 1 0 0 2 1 1 0 0 Depth: 17 | 1345| 2 0 1 1 1 0 0 0 0 Depth: 18 | 269| 0 2 0 0 0 1 0 0 1 Depth: 19 | 3458| 0 0 1 1 1 0 0 1 0 Depth: 20 | 169| 1 0 0 0 0 2 0 0 1 Depth: 21 | 38| 0 0 3 0 0 0 0 1 0 Depth: 22 | 67| 0 0 0 0 0 3 1 0 0 Depth: 23 | 134| 1 0 3 1 0 0 0 0 0 Depth: 24 | 268| 0 1 0 0 0 3 0 1 0 Depth: 25 | 356| 0 0 3 0 1 1 0 0 0 Depth: 26 | 1267| 1 1 0 0 0 2 1 0 0 Depth: 27 | 2345| 0 1 2 1 1 0 0 0 0 Depth: 28 | 469| 0 0 0 1 0 2 0 0 1 Depth: 29 | 389| 0 0 2 0 0 0 0 1 1 Depth: 30 | 678| 0 0 0 0 0 1 2 1 0 Depth: 31 | 1356| 1 0 1 0 2 1 0 0 0 Depth: 32 | 127| 2 2 0 0 0 0 1 0 0 Depth: 33 | 245| 0 2 0 2 1 0 0 0 0 Depth: 34 | 489| 0 0 0 2 0 0 0 1 1 Depth: 35 | 789| 0 0 0 0 0 0 1 2 1 Depth: 36 | 1578| 1 0 0 0 1 0 2 1 0 Depth: 37 | 1356| 1 0 1 0 2 1 0 0 0 The above is the same as one at depth 31 Cyclic. length=6 inductions=0// From (d=0) | 7| 0 0 0 0 0 0 4 0 0 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=3),L1=4 (d=4). L1>=5 Depth: 5 | 1289| 1 2 0 0 0 0 0 L1-4 1 , L1>=5 Depth: 6 | 24578| 0 1 0 1 1 0 L1-4 1 0 , L1>=5 Depth: 7 | 14569| 1 0 0 1 L1-4 1 0 0 1 , L1>=5 Depth: 8 | 12389|L1-4 1 1 0 0 0 0 1 1 , L1>=5 Depth: 9 | 2478| 0 L1-4 0 1 0 0 2 1 0 , L1>=5 Depth: 10 | 4569| 0 0 0 L1-4 2 1 0 0 1 , L1>=5 Depth: 11 | 1389| 2 0 1 0 0 0 0 L1-4 1 , L1>=5 Depth: 12 | 278| 0 2 0 0 0 0 L1-3 1 0 , L1>=5 Depth: 13 | 456| 0 0 0 1 L1-2 1 0 0 0 , L1>=5 Depth: 14 | 129|L1-2 1 0 0 0 0 0 0 1 , L1>=5 The above is the same as one at depth 2 Cyclic. length=12 inductions=0// From (d=0) | 7| 0 0 0 0 0 0 L1 0 0 , L1>=5 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=3),L1>=5 (d=4). Initial number Depth: 0 | 8| 0 0 0 0 0 0 0 L1 0 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 0 | 8| 0 0 0 0 0 0 0 1 0 Depth: 1 | 16| 1 0 0 0 0 1 0 0 0 Depth: 2 | 23| 0 1 1 0 0 0 0 0 0 Depth: 3 | 46| 0 0 0 1 0 1 0 0 0 Depth: 4 | 29| 0 1 0 0 0 0 0 0 1 Depth: 5 | 58| 0 0 0 0 1 0 0 1 0 Depth: 6 | 16| 2 0 0 0 0 1 0 0 0 Depth: 7 | 23| 0 2 1 0 0 0 0 0 0 Depth: 8 | 46| 0 0 0 2 0 1 0 0 0 Depth: 9 | 289| 0 1 0 0 0 0 0 1 1 Depth: 10 | 578| 0 0 0 0 1 0 1 1 0 Depth: 11 | 156| 2 0 0 0 1 1 0 0 0 Depth: 12 | 123| 1 2 1 0 0 0 0 0 0 Depth: 13 | 246| 0 1 0 2 0 1 0 0 0 Depth: 14 | 2489| 0 1 0 1 0 0 0 1 1 Depth: 15 | 4789| 0 0 0 1 0 0 1 1 1 Depth: 16 | 5789| 0 0 0 0 1 0 1 1 1 Depth: 17 | 1578| 2 0 0 0 1 0 1 1 0 Depth: 18 | 12356| 1 1 1 0 1 1 0 0 0 Depth: 19 | 1247| 1 2 0 1 0 0 1 0 0 Depth: 20 | 249| 0 1 0 3 0 0 0 0 1 Depth: 21 | 489| 0 0 0 1 0 0 0 3 1 Depth: 22 | 789| 0 0 0 0 0 0 3 1 1 Depth: 23 | 1578| 1 0 0 0 3 0 1 1 0 Depth: 24 | 1356| 3 0 1 0 1 1 0 0 0 Depth: 25 | 127| 1 4 0 0 0 0 1 0 0 Depth: 26 | 245| 0 1 0 4 1 0 0 0 0 Depth: 27 | 489| 0 0 0 1 0 0 0 3 1 The above is the same as one at depth 21 Cyclic. length=6 inductions=0// From (d=0) | 8| 0 0 0 0 0 0 0 1 0 conditions:L1=1 (d=0). L1>=2 Depth: 1 | 167| 1 0 0 0 0 1 L1-1 0 0 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 1 | 167| 1 0 0 0 0 1 1 0 0 Depth: 2 | 34| 0 0 2 1 0 0 0 0 0 Depth: 3 | 68| 0 0 0 0 0 2 0 1 0 Depth: 4 | 136| 1 0 2 0 0 1 0 0 0 Depth: 5 | 267| 0 2 0 0 0 1 1 0 0 Depth: 6 | 345| 0 0 1 2 1 0 0 0 0 Depth: 7 | 689| 0 0 0 0 0 1 0 1 1 Depth: 8 | 1378| 1 0 1 0 0 0 1 1 0 Depth: 9 | 2567| 0 1 0 0 1 1 1 0 0 Depth: 10 | 1345| 1 0 1 1 1 0 0 0 0 Depth: 11 | 269| 0 1 0 0 0 1 0 0 1 Depth: 12 | 358| 0 0 1 0 1 0 0 1 0 Depth: 13 | 167| 1 0 0 0 0 1 1 0 0 The above is the same as one at depth 1 Cyclic. length=12 inductions=0// From (d=0) | 8| 0 0 0 0 0 0 0 2 0 conditions:L1>=2 (d=0),L1=2 (d=1). L1>=3 Depth: 2 | 345| 0 0 2 1 L1-2 0 0 0 0 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 2 | 345| 0 0 2 1 1 0 0 0 0 Depth: 3 | 69| 0 0 0 0 0 2 0 0 1 Depth: 4 | 138| 1 0 2 0 0 0 0 1 0 Depth: 5 | 267| 0 1 0 0 0 2 1 0 0 Depth: 6 | 345| 0 0 2 1 1 0 0 0 0 The above is the same as one at depth 2 Cyclic. length=4 inductions=0// From (d=0) | 8| 0 0 0 0 0 0 0 3 0 conditions:L1>=2 (d=0),L1>=3 (d=1),L1=3 (d=2). L1>=4 Depth: 3 | 169|L1-3 0 0 0 0 2 0 0 1 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 3 | 169| 1 0 0 0 0 2 0 0 1 Depth: 4 | 38| 0 0 3 0 0 0 0 1 0 Depth: 5 | 67| 0 0 0 0 0 3 1 0 0 Depth: 6 | 134| 1 0 3 1 0 0 0 0 0 Depth: 7 | 268| 0 1 0 0 0 3 0 1 0 Depth: 8 | 356| 0 0 3 0 1 1 0 0 0 Depth: 9 | 1267| 1 1 0 0 0 2 1 0 0 Depth: 10 | 2345| 0 1 2 1 1 0 0 0 0 Depth: 11 | 469| 0 0 0 1 0 2 0 0 1 Depth: 12 | 389| 0 0 2 0 0 0 0 1 1 Depth: 13 | 678| 0 0 0 0 0 1 2 1 0 Depth: 14 | 1356| 1 0 1 0 2 1 0 0 0 Depth: 15 | 127| 2 2 0 0 0 0 1 0 0 Depth: 16 | 245| 0 2 0 2 1 0 0 0 0 Depth: 17 | 489| 0 0 0 2 0 0 0 1 1 Depth: 18 | 789| 0 0 0 0 0 0 1 2 1 Depth: 19 | 1578| 1 0 0 0 1 0 2 1 0 Depth: 20 | 1356| 1 0 1 0 2 1 0 0 0 The above is the same as one at depth 14 Cyclic. length=6 inductions=0// From (d=0) | 8| 0 0 0 0 0 0 0 4 0 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1=4 (d=3). L1>=5 Depth: 4 | 238| 0 L1-4 3 0 0 0 0 1 0 , L1>=5 Depth: 5 | 467| 0 0 0 L1-4 0 3 1 0 0 , L1>=5 Branch: L1=5(fix) or >=6 L1=5 Depth: 5 | 467| 0 0 0 1 0 3 1 0 0 Depth: 6 | 349| 0 0 3 1 0 0 0 0 1 Depth: 7 | 689| 0 0 0 0 0 3 0 1 1 Depth: 8 | 1378| 1 0 3 0 0 0 1 1 0 Depth: 9 | 2567| 0 1 0 0 1 3 1 0 0 Depth: 10 | 1345| 1 0 3 1 1 0 0 0 0 Depth: 11 | 269| 0 1 0 0 0 3 0 0 1 Depth: 12 | 358| 0 0 3 0 1 0 0 1 0 Depth: 13 | 167| 1 0 0 0 0 3 1 0 0 Depth: 14 | 34| 0 0 4 1 0 0 0 0 0 Depth: 15 | 68| 0 0 0 0 0 4 0 1 0 Depth: 16 | 136| 1 0 4 0 0 1 0 0 0 Depth: 17 | 267| 0 2 0 0 0 3 1 0 0 Depth: 18 | 345| 0 0 3 2 1 0 0 0 0 Depth: 19 | 689| 0 0 0 0 0 3 0 1 1 The above is the same as one at depth 7 Cyclic. length=12 inductions=0// From (d=0) | 8| 0 0 0 0 0 0 0 5 0 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1>=5 (d=3),L1=5 (d=5). L1>=6 Depth: 6 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 Depth: 7 | 6789| 0 0 0 0 0 3 L1-5 1 1 , L1>=6 Depth: 8 | 13578| 1 0 3 0 L1-5 0 1 1 0 , L1>=6 Depth: 9 | 12567|L1-5 1 0 0 1 3 1 0 0 , L1>=6 Depth: 10 | 12345| 1 L1-5 3 1 1 0 0 0 0 , L1>=6 Depth: 11 | 2469| 0 1 0 L1-5 0 3 0 0 1 , L1>=6 Depth: 12 | 3489| 0 0 3 1 0 0 0 L1-5 1 , L1>=6 The above is the same as one at depth 6 Cyclic. length=6 inductions=0// From (d=0) | 8| 0 0 0 0 0 0 0 L1 0 , L1>=6 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1>=5 (d=3),L1>=6 (d=5). Initial number Depth: 0 | 9| 0 0 0 0 0 0 0 0 L1 , L1>=1 Branch: L1=1(fix) or >=2 L1=1 Depth: 0 | 9| 0 0 0 0 0 0 0 0 1 Depth: 1 | 18| 1 0 0 0 0 0 0 1 0 Depth: 2 | 36| 0 0 1 0 0 1 0 0 0 Depth: 3 | 27| 0 1 0 0 0 0 1 0 0 Depth: 4 | 45| 0 0 0 1 1 0 0 0 0 Depth: 5 | 9| 0 0 0 0 0 0 0 0 1 The above is the same as one at depth 0 Cyclic. length=5 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 1 conditions:L1=1 (d=0). L1>=2 Depth: 1 | 189| 1 0 0 0 0 0 0 1 L1-1 , L1>=2 Branch: L1=2(fix) or >=3 L1=2 Depth: 1 | 189| 1 0 0 0 0 0 0 1 1 Depth: 2 | 378| 0 0 1 0 0 0 1 1 0 Depth: 3 | 567| 0 0 0 0 1 1 1 0 0 Depth: 4 | 134| 2 0 1 1 0 0 0 0 0 Depth: 5 | 268| 0 2 0 0 0 1 0 1 0 Depth: 6 | 3456| 0 0 1 1 1 1 0 0 0 Depth: 7 | 1269| 1 1 0 0 0 1 0 0 1 Depth: 8 | 2358| 0 1 1 0 1 0 0 1 0 Depth: 9 | 1467| 1 0 0 1 0 1 1 0 0 Depth: 10 | 2349| 0 1 1 1 0 0 0 0 1 Depth: 11 | 4689| 0 0 0 1 0 1 0 1 1 Depth: 12 | 3789| 0 0 1 0 0 0 1 1 1 Depth: 13 | 578| 0 0 0 0 1 0 2 1 0 Depth: 14 | 156| 2 0 0 0 2 1 0 0 0 Depth: 15 | 123| 2 2 1 0 0 0 0 0 0 Depth: 16 | 246| 0 2 0 2 0 1 0 0 0 Depth: 17 | 2489| 0 1 0 2 0 0 0 1 1 Depth: 18 | 4789| 0 0 0 1 0 0 1 2 1 Depth: 19 | 5789| 0 0 0 0 1 0 2 1 1 Depth: 20 | 1578| 2 0 0 0 2 0 1 1 0 Depth: 21 | 12356| 2 1 1 0 1 1 0 0 0 Depth: 22 | 1247| 1 3 0 1 0 0 1 0 0 Depth: 23 | 249| 0 1 0 4 0 0 0 0 1 Depth: 24 | 489| 0 0 0 1 0 0 0 4 1 Depth: 25 | 789| 0 0 0 0 0 0 4 1 1 Depth: 26 | 1578| 1 0 0 0 4 0 1 1 0 Depth: 27 | 1356| 4 0 1 0 1 1 0 0 0 Depth: 28 | 127| 1 5 0 0 0 0 1 0 0 Depth: 29 | 245| 0 1 0 5 1 0 0 0 0 Depth: 30 | 489| 0 0 0 1 0 0 0 4 1 The above is the same as one at depth 24 Cyclic. length=6 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 2 conditions:L1>=2 (d=0),L1=2 (d=1). L1>=3 Depth: 2 | 3789| 0 0 1 0 0 0 1 1 L1-2 , L1>=3 Branch: L1=3(fix) or >=4 L1=3 Depth: 2 | 3789| 0 0 1 0 0 0 1 1 1 Depth: 3 | 578| 0 0 0 0 1 0 2 1 0 Depth: 4 | 156| 2 0 0 0 2 1 0 0 0 Depth: 5 | 123| 2 2 1 0 0 0 0 0 0 Depth: 6 | 246| 0 2 0 2 0 1 0 0 0 Depth: 7 | 2489| 0 1 0 2 0 0 0 1 1 Depth: 8 | 4789| 0 0 0 1 0 0 1 2 1 Depth: 9 | 5789| 0 0 0 0 1 0 2 1 1 Depth: 10 | 1578| 2 0 0 0 2 0 1 1 0 Depth: 11 | 12356| 2 1 1 0 1 1 0 0 0 Depth: 12 | 1247| 1 3 0 1 0 0 1 0 0 Depth: 13 | 249| 0 1 0 4 0 0 0 0 1 Depth: 14 | 489| 0 0 0 1 0 0 0 4 1 Depth: 15 | 789| 0 0 0 0 0 0 4 1 1 Depth: 16 | 1578| 1 0 0 0 4 0 1 1 0 Depth: 17 | 1356| 4 0 1 0 1 1 0 0 0 Depth: 18 | 127| 1 5 0 0 0 0 1 0 0 Depth: 19 | 245| 0 1 0 5 1 0 0 0 0 Depth: 20 | 489| 0 0 0 1 0 0 0 4 1 The above is the same as one at depth 14 Cyclic. length=6 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 3 conditions:L1>=2 (d=0),L1>=3 (d=1),L1=3 (d=2). L1>=4 Depth: 3 | 5789| 0 0 0 0 1 0 2 1 L1-3 , L1>=4 Branch: L1=4(fix) or >=5 L1=4 Depth: 3 | 5789| 0 0 0 0 1 0 2 1 1 Depth: 4 | 1578| 2 0 0 0 2 0 1 1 0 Depth: 5 | 12356| 2 1 1 0 1 1 0 0 0 Depth: 6 | 1247| 1 3 0 1 0 0 1 0 0 Depth: 7 | 249| 0 1 0 4 0 0 0 0 1 Depth: 8 | 489| 0 0 0 1 0 0 0 4 1 Depth: 9 | 789| 0 0 0 0 0 0 4 1 1 Depth: 10 | 1578| 1 0 0 0 4 0 1 1 0 Depth: 11 | 1356| 4 0 1 0 1 1 0 0 0 Depth: 12 | 127| 1 5 0 0 0 0 1 0 0 Depth: 13 | 245| 0 1 0 5 1 0 0 0 0 Depth: 14 | 489| 0 0 0 1 0 0 0 4 1 The above is the same as one at depth 8 Cyclic. length=6 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 4 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1=4 (d=3). L1>=5 Depth: 4 | 15789| 2 0 0 0 2 0 1 1 L1-4 , L1>=5 Branch: L1=5(fix) or >=6 L1=5 Depth: 4 | 15789| 2 0 0 0 2 0 1 1 1 Depth: 5 | 123578| 2 1 1 0 1 0 1 1 0 Depth: 6 | 124567| 1 2 0 1 1 1 1 0 0 Depth: 7 | 12349| 1 1 1 3 0 0 0 0 1 Depth: 8 | 24689| 0 1 0 1 0 1 0 3 1 Depth: 9 | 34789| 0 0 1 1 0 0 3 1 1 Depth: 10 | 56789| 0 0 0 0 3 1 1 1 1 Depth: 11 | 13578| 4 0 1 0 1 0 1 1 0 Depth: 12 | 12567| 1 4 0 0 1 1 1 0 0 Depth: 13 | 12345| 1 1 1 4 1 0 0 0 0 Depth: 14 | 24689| 0 1 0 1 0 1 0 3 1 The above is the same as one at depth 8 Cyclic. length=6 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 5 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1>=5 (d=3),L1=5 (d=4). L1>=6 Depth: 5 | 1235789| 2 1 1 0 1 0 1 1 L1-5 , L1>=6 Branch: L1=6(fix) or >=7 L1=6 Depth: 5 | 1235789| 2 1 1 0 1 0 1 1 1 Depth: 6 | 124578| 1 2 0 1 1 0 2 1 0 Depth: 7 | 124569| 1 1 0 2 2 1 0 0 1 Depth: 8 | 123489| 2 1 1 1 0 0 0 2 1 Depth: 9 | 246789| 0 2 0 1 0 1 2 1 1 Depth: 10 | 345789| 0 0 1 2 2 0 1 1 1 Depth: 11 | 156789| 2 0 0 0 1 1 1 2 1 Depth: 12 | 123578| 1 1 2 0 1 0 2 1 0 Depth: 13 | 124567| 1 1 0 1 2 2 1 0 0 Depth: 14 | 12349| 2 1 2 2 0 0 0 0 1 Depth: 15 | 24689| 0 2 0 1 0 2 0 2 1 Depth: 16 | 34789| 0 0 2 2 0 0 2 1 1 Depth: 17 | 56789| 0 0 0 0 2 2 1 2 1 Depth: 18 | 13578| 3 0 2 0 1 0 2 1 0 Depth: 19 | 12567| 1 3 0 0 2 2 1 0 0 Depth: 20 | 12345| 2 1 2 3 1 0 0 0 0 Depth: 21 | 24689| 0 2 0 1 0 2 0 2 1 The above is the same as one at depth 15 Cyclic. length=6 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 6 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1>=5 (d=3),L1>=6 (d=4),L1=6 (d=5). L1>=7 Depth: 6 | 1245789| 1 2 0 1 1 0 2 1 L1-6 , L1>=7 Depth: 7 | 1245789| 1 1 0 2 2 0 1 1 L1-6 , L1>=7 Depth: 8 | 1245789| 2 1 0 1 1 0 1 2 L1-6 , L1>=7 Depth: 9 | 1245789| 1 2 0 1 1 0 2 1 L1-6 , L1>=7 The above is the same as one at depth 6 Cyclic. length=3 inductions=0// From (d=0) | 9| 0 0 0 0 0 0 0 0 L1 , L1>=7 conditions:L1>=2 (d=0),L1>=3 (d=1),L1>=4 (d=2),L1>=5 (d=3),L1>=6 (d=4),L1>=7 (d=5). Found cyclic sequences: 54 Found inductive sequences: 0