Identifier
- St000683: Dyck paths ⟶ ℤ
Values
[1,0,1,0] => 0
[1,1,0,0] => 1
[1,0,1,0,1,0] => 0
[1,0,1,1,0,0] => 1
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 0
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0] => 0
[1,0,1,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,0] => 0
[1,1,0,1,1,0,0,0] => 2
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 4
[1,1,1,0,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,1,0,0,0,0] => 4
[1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,0] => 4
[1,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => 6
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0] => 9
[1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 9
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 4
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 5
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 11
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 4
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 6
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 0
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 0
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 6
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 13
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 6
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 10
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 6
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 11
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 5
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 9
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 9
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 11
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 8
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 8
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 7
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 11
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 7
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 11
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 11
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 14
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 13
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 12
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 2
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 6
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 4
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 2
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 6
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 4
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 3
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 7
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 0
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 2
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 1
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 5
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 2
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 1
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 3
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 2
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 1
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 4
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 8
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 5
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 8
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 7
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 6
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 5
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 2
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 4
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 3
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 2
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 1
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 1
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 0
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 1
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 5
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 4
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 4
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 3
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 1
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 0
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 4
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 3
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 15
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 11
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 10
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 4
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 3
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 4
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 6
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 11
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 3
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 3
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 2
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 5
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 4
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 3
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 2
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 1
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 5
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 4
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 3
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 8
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 16
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 0
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 2
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 1
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 6
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 1
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 2,2,0,1 4,4,3,2,0,0,1 8,11,9,4,5,2,2,0,0,0,1 17,28,22,24,16,6,5,7,2,2,2,0,0,0,0,1 37,67,69,80,40,37,37,24,7,8,5,9,2,2,2,2,0,0,0,0,0,1
$F_{2} = 1 + q$
$F_{3} = 2 + 2\ q + q^{3}$
$F_{4} = 4 + 4\ q + 3\ q^{2} + 2\ q^{3} + q^{6}$
$F_{5} = 8 + 11\ q + 9\ q^{2} + 4\ q^{3} + 5\ q^{4} + 2\ q^{5} + 2\ q^{6} + q^{10}$
$F_{6} = 17 + 28\ q + 22\ q^{2} + 24\ q^{3} + 16\ q^{4} + 6\ q^{5} + 5\ q^{6} + 7\ q^{7} + 2\ q^{8} + 2\ q^{9} + 2\ q^{10} + q^{15}$
$F_{7} = 37 + 67\ q + 69\ q^{2} + 80\ q^{3} + 40\ q^{4} + 37\ q^{5} + 37\ q^{6} + 24\ q^{7} + 7\ q^{8} + 8\ q^{9} + 5\ q^{10} + 9\ q^{11} + 2\ q^{12} + 2\ q^{13} + 2\ q^{14} + 2\ q^{15} + q^{21}$
Description
The number of points below the Dyck path such that the diagonal to the north-east hits the path between two down steps, and the diagonal to the north-west hits the path between two up steps.
References
[1] Mare Counting QF-1 algebras inside quotient algebras of upper triangular matrices via Dyck paths MathOverflow:259038
Code
def statistic(D):
"""Return the number of points such that the diagonal to the
north-east hits the path between two down steps, and the diagonal
to the north-west hits the path between two up steps.
sage: statistic([1,1,0,1,1,0,1,1,0,0,0,0])
4
sage: [len([D for D in DyckWords(r) if statistic(D) == 0]) for r in range(8)]
[1, 1, 1, 2, 4, 8, 17, 37, 81, 179]
"""
D = DyckWord(D)
H = D.heights()
left_bad_points = [(i+1, H[i+1]) for i in range(len(D)-1) if D[i] == D[i+1] == 1]
right_bad_points = [(i+1, H[i+1]) for i in range(len(D)-1) if D[i] == D[i+1] == 0]
result = 0
for i,h in enumerate(D.heights()):
for j in range(h-2,-1,-2):
if (any((i-a + j-b) == 0 for (a,b) in left_bad_points) and
any((i-a - j+b) == 0 for (a,b) in right_bad_points)):
result += 1
return result
Created
Jan 08, 2017 at 16:14 by Martin Rubey
Updated
Jan 08, 2017 at 16:14 by Martin Rubey
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