Identifier
Values
[1,0,1,0] => [1] => 1
[1,0,1,0,1,0] => [2,1] => 1
[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] => 0
[1,0,1,0,1,1,0,0] => [2,2,1] => 1
[1,0,1,1,0,0,1,0] => [3,1,1] => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => 1
[1,0,1,1,1,0,0,0] => [1,1,1] => 3
[1,1,0,0,1,0,1,0] => [3,2] => 0
[1,1,0,0,1,1,0,0] => [2,2] => 1
[1,1,0,1,0,0,1,0] => [3,1] => 0
[1,1,0,1,0,1,0,0] => [2,1] => 1
[1,1,0,1,1,0,0,0] => [1,1] => 1
[1,1,1,0,0,0,1,0] => [3] => 0
[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] => 0
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => 1
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => 0
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => 9
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => 0
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => 0
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => 1
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => 0
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => 1
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => 3
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => 0
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => 9
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => 0
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => 0
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => 1
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => 0
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => 9
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => 0
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => 0
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => 1
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => 1
[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] => 0
[1,1,1,0,0,0,1,1,0,0] => [3,3] => 0
[1,1,1,0,0,1,0,0,1,0] => [4,2] => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => 0
[1,1,1,0,0,1,1,0,0,0] => [2,2] => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => 1
[1,1,1,0,1,0,0,1,0,0] => [3,1] => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => 1
[1,1,1,0,1,1,0,0,0,0] => [1,1] => 1
[1,1,1,1,0,0,0,0,1,0] => [4] => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => 0
[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] => 33
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => 9
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => 0
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => 3
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => 3
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => 9
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => 9
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => 21
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => 0
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => 33
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => 0
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => 0
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => 9
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => 1
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => 3
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => 3
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => 9
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => 18
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => 0
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => 0
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => 1
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => 0
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => 9
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => 1
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => 0
>>> Load all 448 entries. <<<
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => 1
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => 1
[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] => 1
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => 1
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => 0
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => 0
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => 0
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => 0
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => 1
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => 1
[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] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => 0
[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] => 27
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => 0
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => 21
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => 81
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => 33
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => 9
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => 0
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => 3
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => 0
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => 3
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => 9
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => 9
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => 21
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => 0
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => 33
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => 0
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => 1
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => 0
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => 9
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => 0
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => 3
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => 3
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => 9
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => 18
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => 0
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => 0
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => 1
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => 0
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => 9
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => 1
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => 0
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => 1
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => 1
[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] => 1
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => 0
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => 0
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => 0
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => 0
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => 0
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => 1
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => 1
[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] => 0
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => 0
[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] => 21
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => 0
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => 81
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => 351
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => 27
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => 0
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => 9
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => 21
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 81
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => 33
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => 9
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => 3
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => 0
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => 3
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => 9
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => 9
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => 21
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => 0
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => 33
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => 0
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => 1
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => 0
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => 9
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => 3
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => 9
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => 18
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => 0
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => 0
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => 1
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => 1
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => 0
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => 9
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => 0
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => 1
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => 1
[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] => 1
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => 0
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => 0
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => 0
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => 0
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => 1
[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] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => 0
[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] => 1
[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] => 1233
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => 1
[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] => 351
[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] => 5769
[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] => 21
[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] => 0
[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] => 81
[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] => 351
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => 27
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => 9
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => 21
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => 0
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => 21
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => 81
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => 33
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => 9
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => 0
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => 3
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => 9
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => 9
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => 21
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => 0
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => 1
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => 0
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => 9
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => 0
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => 0
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => 1
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => 0
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => 3
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => 9
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => 18
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => 0
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => 0
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => 1
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => 0
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => 9
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => 1
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => 0
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => 1
[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] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => 0
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => 1
[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] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => 0
[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] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => 0
[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] => 1233
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => 1
[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] => 9
[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] => 21
[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] => 81
[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] => 351
[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] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => 0
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => 0
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => 0
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => 18
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => 1
[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] => 351
[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] => 5769
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => 0
[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] => 21
[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] => 0
[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] => 21
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => 0
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => 0
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => 9
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => 3
[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] => 9
[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] => 81
[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] => 1
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => 0
[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] => 0
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => 1
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => 0
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => 0
[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] => 0
[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] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => 1
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => 0
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => 9
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => 0
search for individual values
searching the database for the individual values of this statistic
Description
The number of permutations whose cube equals a fixed permutation of given cycle type.
For example, the permutation $\pi=412365$ has cycle type $(4,2)$ and $234165$ is the unique permutation whose cube is $\pi$.
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 $(n-1,\ldots,2,1)$.