Identifier
Values
[1,1] => [1,0,1,0] => 1
[2] => [1,1,0,0] => 0
[1,1,1] => [1,0,1,0,1,0] => 4
[1,2] => [1,0,1,1,0,0] => 2
[2,1] => [1,1,0,0,1,0] => 2
[3] => [1,1,1,0,0,0] => 0
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 13
[1,1,2] => [1,0,1,0,1,1,0,0] => 8
[1,2,1] => [1,0,1,1,0,0,1,0] => 9
[1,3] => [1,0,1,1,1,0,0,0] => 3
[2,1,1] => [1,1,0,0,1,0,1,0] => 8
[2,2] => [1,1,0,0,1,1,0,0] => 5
[3,1] => [1,1,1,0,0,0,1,0] => 3
[4] => [1,1,1,1,0,0,0,0] => 0
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 41
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 27
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 31
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 13
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 31
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 21
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 16
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 27
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 18
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 21
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 9
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 13
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 9
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
[5] => [1,1,1,1,1,0,0,0,0,0] => 0
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 131
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 89
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 103
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 47
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 106
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 74
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 61
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 19
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 103
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 71
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 83
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 39
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 61
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 44
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 25
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 89
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 61
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 71
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 33
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 74
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 52
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 44
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 14
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 47
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 33
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 39
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 19
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 19
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 14
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 428
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 296
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 344
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 164
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 358
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 254
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 218
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 74
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 358
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 251
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 294
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 144
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 232
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 170
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 106
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 26
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 344
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 240
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 280
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 136
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 294
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 210
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 184
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 64
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 218
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 156
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 184
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 94
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 106
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 80
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 36
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 296
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 206
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 240
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 116
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 251
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 179
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 156
>>> Load all 222 entries. <<<
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 54
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 254
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 179
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 210
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 104
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 170
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 125
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 80
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 20
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 164
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 116
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 136
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 68
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 144
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 104
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 94
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 34
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 74
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 54
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 64
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 34
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 26
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 20
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 0
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1429
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1000
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1165
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 571
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1219
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 874
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 769
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 274
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1233
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 874
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1025
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 515
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 841
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 622
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 409
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 109
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1219
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 860
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1005
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 501
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1059
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 764
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 684
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 249
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 841
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 608
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 717
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 375
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 449
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 342
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 169
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 34
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1165
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 820
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 957
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 475
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1005
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 724
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 645
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 234
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1025
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 730
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 857
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 435
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 717
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 532
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 357
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 97
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 769
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 550
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 645
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 331
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 684
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 499
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 459
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 174
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 409
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 302
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 357
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 195
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 169
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 132
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 49
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1000
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 703
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 820
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 406
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 860
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 619
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 550
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 199
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 874
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 622
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 730
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 370
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 608
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 451
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 302
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 82
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 874
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 619
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 724
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 364
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 764
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 553
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 499
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 184
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 622
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 451
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 532
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 280
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 342
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 261
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 132
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 27
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Description
The number of Dyck paths that are weakly above the Dyck path, except for the path itself.
Map
bounce path
Description
The bounce path determined by an integer composition.