Identifier
Values
[1,0,1,0] => [1] => 1
[1,0,1,0,1,0] => [2,1] => 2
[1,0,1,1,0,0] => [1,1] => 1
[1,1,0,0,1,0] => [2] => 1
[1,1,0,1,0,0] => [1] => 1
[1,0,1,0,1,0,1,0] => [3,2,1] => 134
[1,0,1,0,1,1,0,0] => [2,2,1] => 37
[1,0,1,1,0,0,1,0] => [3,1,1] => 26
[1,0,1,1,0,1,0,0] => [2,1,1] => 9
[1,0,1,1,1,0,0,0] => [1,1,1] => 3
[1,1,0,0,1,0,1,0] => [3,2] => 15
[1,1,0,0,1,1,0,0] => [2,2] => 6
[1,1,0,1,0,0,1,0] => [3,1] => 4
[1,1,0,1,0,1,0,0] => [2,1] => 2
[1,1,0,1,1,0,0,0] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => 1
[1,1,1,0,0,1,0,0] => [2] => 1
[1,1,1,0,1,0,0,0] => [1] => 1
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => 79629
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 61417
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 12765
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 2365
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 42080
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 8786
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 6817
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 1636
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 359
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 888
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 251
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 67
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 16
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 21715
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 4562
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 3559
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 861
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 195
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 2445
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 596
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 469
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 134
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 37
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 75
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 26
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 9
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => 3
[1,1,1,0,0,0,1,0,1,0] => [4,3] => 175
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 51
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 43
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 15
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 6
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 9
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 4
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 2
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 2
[1,1,1,1,0,0,0,1,0,0] => [3] => 1
[1,1,1,1,0,0,1,0,0,0] => [2] => 1
[1,1,1,1,0,1,0,0,0,0] => [1] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => 330685
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 226225
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 35892
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 154833
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 119325
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 24674
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 4530
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 51873
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 13155
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 3135
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 680
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 125
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 116314
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 18584
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 79629
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 61417
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 12765
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 2365
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 42080
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 8786
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 26736
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 6817
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 1636
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 359
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 3023
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 888
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 251
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 67
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 16
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 28110
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 21715
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 4562
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 13820
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 3559
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 861
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 195
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 11513
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 9480
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 2445
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 596
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 1577
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 469
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 134
>>> Load all 448 entries. <<<
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 37
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 214
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 75
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 26
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 9
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => 2626
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 698
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 573
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 175
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 51
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 116
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 43
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 15
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 6
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 20
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 9
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 4
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 2
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => 3
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 2
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [1] => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => 644190
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 440542
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 69552
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 232154
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 47787
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 8716
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1296
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 330685
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 226225
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 35892
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 154833
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 119325
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 24674
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 4530
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 51873
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 13155
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 3135
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 680
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 125
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 116314
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 18584
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 79629
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 61417
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 12765
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 2365
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 42080
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 8786
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 26736
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 6817
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 1636
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 359
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 10038
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 3023
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 888
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 251
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 67
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 16
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 28110
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 21715
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 4562
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 13820
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 3559
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 861
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 195
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 11513
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 9480
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 2445
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 596
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 5204
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 1577
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 469
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 134
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 37
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 612
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 214
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 75
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 26
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 9
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => 2626
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 698
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 1866
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 573
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 175
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 51
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 329
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 116
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 43
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 15
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 48
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 20
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 9
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => 6
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [1] => 1
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 1255973
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 858578
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 134960
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 16807
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 644190
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 440542
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 69552
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 232154
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 47787
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 8716
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1296
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 330685
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 226225
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 35892
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 154833
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 119325
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 24674
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 4530
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 51873
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 13155
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 3135
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 680
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 125
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 116314
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 18584
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 79629
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 61417
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 12765
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 2365
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 42080
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 8786
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 26736
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 6817
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 1636
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 359
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 10038
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 3023
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 888
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 251
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 67
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 16
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 28110
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 21715
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 4562
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 13820
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 3559
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 861
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 195
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 11513
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 9480
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 2445
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 596
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 5204
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 1577
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 469
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 134
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 37
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1747
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 612
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 214
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 75
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 26
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 9
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => 2626
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 698
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 1866
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 573
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 175
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 51
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 918
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 329
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 116
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 43
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 15
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 6
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 115
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 48
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 20
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 9
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => 11
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 6
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 2
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => 23
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 262144
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 47
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 286
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 2450309
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 4782969
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => 1255973
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => 858578
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 134960
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 16807
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 644190
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 440542
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 69552
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 232154
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 47787
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 8716
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1296
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 330685
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 226225
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 35892
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 154833
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 24674
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 4530
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 51873
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 680
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 125
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 79629
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 61417
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 12765
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 2365
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 42080
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 8786
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 6817
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 1636
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 359
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 10038
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 3023
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 888
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 251
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 67
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 16
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 28110
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 21715
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 4562
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 3559
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 861
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 195
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 11513
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 9480
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 2445
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 596
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 5204
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 1577
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 469
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 134
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 37
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 1747
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 612
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 75
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 26
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 9
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => 3
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => 698
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 175
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 51
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 918
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 43
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 15
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 6
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 115
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 48
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 20
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 9
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => 11
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 6
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 3
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 2
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => 37
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 15
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => 1
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => 262144
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 23
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 47
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 286
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => 3
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => 16
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 125
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 1296
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 16807
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0] => [1] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => 11
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 2
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 6
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 51
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 28110
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 9
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => 2450309
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => 4782969
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 21715
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 8716
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => 47787
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => 232154
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 2
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 134
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 4
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 43
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 2445
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 195
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 115
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 48
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 20
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 9
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 67
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => 680
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 134960
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => 9
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 12765
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => 3
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => 26
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 359
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 1636
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 6
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 51
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => 1
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => 286
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 115
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 48
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 20
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 9
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 698
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 9480
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 2365
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 4562
search for individual values
searching the database for the individual values of this statistic
Description
The number of coloured trees such that the multiplicities of colours are given by a partition.
In particular, the value on the partition $(n)$ is the number of unlabelled trees on $n$ vertices, oeis:A000055, whereas the value on the partition $(1^n)$ is the number of labelled trees oeis:A000272.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.