Identifier
Values
[1,1] => [1,0,1,0] => 0
[2] => [1,1,0,0] => 0
[1,1,1] => [1,0,1,0,1,0] => 0
[1,2] => [1,0,1,1,0,0] => 0
[2,1] => [1,1,0,0,1,0] => 0
[3] => [1,1,1,0,0,0] => 1
[1,1,1,1] => [1,0,1,0,1,0,1,0] => 0
[1,1,2] => [1,0,1,0,1,1,0,0] => 0
[1,2,1] => [1,0,1,1,0,0,1,0] => 0
[1,3] => [1,0,1,1,1,0,0,0] => 1
[2,1,1] => [1,1,0,0,1,0,1,0] => 0
[2,2] => [1,1,0,0,1,1,0,0] => 0
[3,1] => [1,1,1,0,0,0,1,0] => 1
[4] => [1,1,1,1,0,0,0,0] => 2
[1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 0
[1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 0
[1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 0
[1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 0
[1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 1
[1,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 0
[2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 0
[2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 0
[2,3] => [1,1,0,0,1,1,1,0,0,0] => 1
[3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 1
[3,2] => [1,1,1,0,0,0,1,1,0,0] => 1
[4,1] => [1,1,1,1,0,0,0,0,1,0] => 2
[5] => [1,1,1,1,1,0,0,0,0,0] => 3
[1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 3
[2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 0
[2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 0
[2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 0
[2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 0
[2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 0
[2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 2
[3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 1
[3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 1
[3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 1
[3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 2
[4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 2
[4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 2
[5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 3
[6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
>>> Load all 222 entries. <<<
[2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,1,1,2,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,1,1,2,3] => [1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,1,1,3,1,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,1,1,4,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[1,1,2,1,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[1,1,2,1,3] => [1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[1,1,2,2,1,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[1,1,2,3,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,3,1,2] => [1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[1,1,3,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[1,1,4,1,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
[1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 0
[1,2,1,1,2,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 0
[1,2,1,1,3] => [1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 1
[1,2,1,2,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 0
[1,2,1,2,2] => [1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 0
[1,2,1,3,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 1
[1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 2
[1,2,2,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 0
[1,2,2,1,2] => [1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 0
[1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 0
[1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 1
[1,2,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 1
[1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 1
[1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 2
[1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 3
[1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 1
[1,3,1,1,2] => [1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 1
[1,3,1,2,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 1
[1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 2
[1,3,2,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 1
[1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 1
[1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 2
[1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 3
[1,4,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 2
[1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 2
[1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 2
[1,4,3] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 3
[1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 3
[1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 3
[1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 4
[1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 5
[2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 0
[2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 0
[2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 1
[2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 0
[2,1,1,2,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 0
[2,1,1,3,1] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 1
[2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 2
[2,1,2,1,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 0
[2,1,2,1,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 0
[2,1,2,2,1] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 0
[2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 1
[2,1,3,1,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 1
[2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 1
[2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 2
[2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 3
[2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 0
[2,2,1,1,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 0
[2,2,1,2,1] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 0
[2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 1
[2,2,2,1,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 0
[2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 0
[2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 1
[2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 2
[2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 1
[2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 1
[2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 1
[2,3,3] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 2
[2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 2
[2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 2
[2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 3
[2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 4
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Description
The number of occurrences of the pattern UUU in a Dyck path.
The number of Dyck paths with statistic value 0 are counted by the Motzkin numbers [1].
Map
bounce path
Description
The bounce path determined by an integer composition.