Identifier
Values
[1,1] => [1,0,1,0] => 2
[2] => [1,1,0,0] => 1
[1,1,1] => [1,0,1,0,1,0] => 5
[1,2] => [1,0,1,1,0,0] => 3
[2,1] => [1,1,0,0,1,0] => 3
[3] => [1,1,1,0,0,0] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 14
[1,1,2] => [1,0,1,0,1,1,0,0] => 9
[1,2,1] => [1,0,1,1,0,0,1,0] => 10
[1,3] => [1,0,1,1,1,0,0,0] => 4
[2,1,1] => [1,1,0,0,1,0,1,0] => 9
[2,2] => [1,1,0,0,1,1,0,0] => 6
[3,1] => [1,1,1,0,0,0,1,0] => 4
[4] => [1,1,1,1,0,0,0,0] => 1
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 42
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 28
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 32
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 14
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 32
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 22
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 17
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 28
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 19
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 22
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 10
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 14
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 10
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
[5] => [1,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 132
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 90
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 104
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 48
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 107
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 75
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 62
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 20
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 104
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 72
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 84
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 40
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 62
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 45
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 26
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 90
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 62
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 72
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 34
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 75
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 53
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 45
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 15
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 48
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 34
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 40
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 20
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 20
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 15
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 429
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 297
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 345
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 165
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 359
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 255
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 219
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 75
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 359
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 252
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 295
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 145
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 233
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 171
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 107
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 27
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 345
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 241
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 281
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 137
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 295
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 211
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 185
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 65
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 219
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 157
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 185
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 95
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 107
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 81
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 37
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 297
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 207
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 241
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 117
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 252
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 180
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 157
>>> Load all 222 entries. <<<
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 55
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 255
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 180
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 211
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 105
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 171
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 126
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 81
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 165
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 117
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 137
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 69
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 145
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 105
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 95
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 75
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 55
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 65
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 27
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1430
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1001
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1166
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 572
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1220
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 875
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 770
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 275
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1234
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 875
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 1026
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 516
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 842
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 623
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 410
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 110
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1220
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 861
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 1006
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 502
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 1060
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 765
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 685
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 250
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 842
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 609
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 718
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 376
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 450
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 343
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 170
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1166
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 821
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 958
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 476
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1006
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 725
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 646
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 235
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1026
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 731
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 858
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 436
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 718
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 533
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 358
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 98
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 770
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 551
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 646
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 332
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 685
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 500
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 460
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 175
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 410
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 303
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 358
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 196
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 170
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 133
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 50
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 8
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1001
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 704
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 821
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 407
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 861
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 620
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 551
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 200
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 875
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 623
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 731
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 371
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 609
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 452
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 303
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 83
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 875
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 620
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 725
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 365
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 765
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 554
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 500
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 185
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 623
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 452
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 533
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 281
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 343
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 262
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 133
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 28
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Description
The number of Dyck paths that are weakly above a Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.