Identifier
- St000976: 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] => 3
[1,1,0,0,1,0] => 1
[1,1,0,1,0,0] => 1
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 0
[1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0] => 7
[1,1,0,0,1,0,1,0] => 1
[1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,0] => 1
[1,1,0,1,1,0,0,0] => 5
[1,1,1,0,0,0,1,0] => 3
[1,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,0] => 3
[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] => 7
[1,0,1,0,1,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0] => 5
[1,0,1,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,1,1,1,0,0,0,0] => 12
[1,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,0,0] => 6
[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] => 9
[1,0,1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,0,1,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,1,0,0,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,0,0,0,0] => 18
[1,0,1,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,0,0,1,1,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,1,0,0,0] => 18
[1,0,1,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,1,0,0] => 12
[1,0,1,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => 11
[1,0,1,1,0,1,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => 16
[1,0,1,1,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,1,0,0] => 16
[1,0,1,1,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,1,0,0,0] => 15
[1,0,1,1,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,0,0,0,1,0] => 12
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,0] => 18
[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] => 10
[1,1,0,0,1,0,1,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,1,0,0,0] => 16
[1,1,0,0,1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,1,0,0] => 15
[1,1,0,0,1,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,0,0] => 14
[1,1,0,0,1,1,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,0] => 19
[1,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,1,0,0] => 10
[1,1,0,1,0,0,1,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => 16
[1,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,1,0,0] => 10
[1,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,0] => 14
[1,1,0,1,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,1,0,0] => 14
[1,1,0,1,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,1,0,0,0] => 13
[1,1,0,1,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,1,0,0,0,0] => 12
[1,1,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,1,0,0,0,0,0] => 16
[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] => 12
[1,1,1,0,0,0,1,1,0,0,1,0] => 10
[1,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => 18
[1,1,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,1,0,0,0] => 11
[1,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,0] => 16
[1,1,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,1,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,0,0,0] => 14
[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] => 15
[1,1,1,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,1,0,0,0] => 14
[1,1,1,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0] => 6
[1,1,1,1,0,0,1,1,0,0,0,0] => 13
[1,1,1,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,1,0,0,0,0] => 6
[1,1,1,1,0,1,1,0,0,0,0,0] => 12
[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] => 10
[1,1,1,1,1,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,0,0] => 10
[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] => 11
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 19
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 18
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 17
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 15
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 24
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 16
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 24
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 16
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 15
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 22
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 22
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 21
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 20
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 18
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 18
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 18
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 18
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 26
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 12
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 12
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 22
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 21
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 20
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 27
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 22
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 13
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 11
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 20
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 19
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 16
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 24
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 18
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 16
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 26
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 18
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 17
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 15
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 15
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 15
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 24
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 18
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 22
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 23
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 22
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 21
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 20
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 25
[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] => 12
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 20
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 19
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 18
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 16
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 16
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 25
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 15
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 25
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 16
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 14
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 14
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 23
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 23
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 22
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 21
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 19
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 19
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 19
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 19
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 27
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 12
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 10
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 20
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 19
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 8
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 18
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 16
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 16
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 16
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 25
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 10
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 10
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 20
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 1
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 1
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 11
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 9
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 18
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 18
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 17
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 16
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 14
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 14
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 14
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 14
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 22
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 16
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 24
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 16
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 15
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 13
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 13
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 13
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 22
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 16
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 15
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 5
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 14
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 12
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 12
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 20
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 21
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 20
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 10
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 19
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 18
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 16
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 16
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 16
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 16
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 16
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 23
[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] => 14
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 12
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 22
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 10
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 21
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 10
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 10
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 20
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 18
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 18
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 18
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 27
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 12
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 22
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 14
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 13
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 11
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 11
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 11
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 20
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 20
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 19
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 9
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 9
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 18
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 16
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 16
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 16
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 16
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 24
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 14
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 12
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 22
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 14
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 13
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 11
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 11
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 11
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 20
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 14
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 13
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 10
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 10
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 18
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 19
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 18
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 8
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 17
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 8
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 16
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 14
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 14
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 14
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 14
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 14
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 21
[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] => 17
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 15
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 15
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 25
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 17
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 16
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 14
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 14
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 14
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 23
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 17
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 16
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 15
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 13
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 13
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 21
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 17
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 16
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 15
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 14
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 12
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 12
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 12
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 12
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 12
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 19
[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] => 21
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 10
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 20
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 10
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 19
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 18
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 10
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 10
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 10
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 10
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 10
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 17
[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] => 15
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 15
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 15
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 15
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 15
[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] => 13
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 11
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 23
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 22
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 21
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 19
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 19
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 19
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 30
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 20
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 18
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 30
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 20
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 19
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 17
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 28
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 15
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 28
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 15
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 15
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 27
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 15
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 15
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 15
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 26
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 24
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 24
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 24
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 24
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 34
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 16
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 28
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 27
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 26
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 24
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 24
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 24
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 35
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 16
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 28
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 18
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 5
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 17
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 15
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 15
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 15
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 26
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 26
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 25
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 24
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 22
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 22
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 22
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 22
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 32
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 24
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 22
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 22
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 34
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 24
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 23
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 21
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 21
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 21
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 32
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 24
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 23
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 22
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 20
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 20
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 20
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 20
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 30
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 18
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 31
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 18
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 18
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 30
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 18
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 18
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 18
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 29
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 18
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 18
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 18
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 18
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 28
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 26
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 26
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 26
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 26
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 26
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 35
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 16
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 26
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 12
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 25
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 12
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 12
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 24
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 22
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 22
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 22
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 33
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 23
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 21
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 21
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 33
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 23
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 22
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 20
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 20
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 20
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 31
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 31
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 30
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 29
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 27
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 27
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 27
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 27
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 37
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 16
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 26
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 25
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 12
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 24
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 22
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 22
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 22
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 33
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 26
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 3
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 13
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 13
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 24
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 11
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 24
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 11
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 23
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 11
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 22
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 20
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 20
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 20
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 20
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 30
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 22
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 20
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 32
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 22
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 21
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 19
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 19
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 19
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 30
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 22
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 21
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 20
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 18
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 18
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 18
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 18
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 28
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 16
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 29
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 16
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 16
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 28
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 16
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 27
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 16
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 26
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 24
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 24
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 24
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 24
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 24
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 33
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 20
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 18
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 30
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 16
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 29
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 16
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 16
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 28
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 26
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 26
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 26
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 37
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 20
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 18
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 30
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 20
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 19
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 17
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 17
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 28
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 15
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 28
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 15
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 27
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 15
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 15
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 15
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 26
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 24
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 24
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 24
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 24
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 34
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 20
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 18
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 18
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 30
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 20
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 19
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 17
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 28
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 20
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 19
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 18
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 16
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 16
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 16
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 26
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 27
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 26
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 14
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 25
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 14
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 24
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 22
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 22
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 22
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 22
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 22
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 31
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 25
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 23
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 23
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 25
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 24
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 22
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 22
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 22
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 33
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 25
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 24
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 23
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 21
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 21
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 21
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 21
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 31
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 25
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 24
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 23
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 22
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 20
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 20
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 20
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 20
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 20
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 29
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 31
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 30
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 18
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 29
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 18
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 28
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 18
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 27
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 25
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 25
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 25
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 25
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 25
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 25
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 33
[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] => 14
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 12
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 12
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 24
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 23
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 22
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 20
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 20
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 20
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 31
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 21
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 19
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 19
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 31
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 21
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 20
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 18
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 18
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 29
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 16
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 29
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 16
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 16
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 28
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 16
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 16
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 16
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 27
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 25
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 25
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 25
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 25
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 35
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 19
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 29
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 28
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 15
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 15
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 27
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 25
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 25
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 25
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 36
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 19
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 17
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 17
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 29
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 19
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 18
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 16
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 16
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 16
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 27
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 14
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 27
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 14
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 26
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 25
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 23
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 23
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 23
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 23
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 33
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 25
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 23
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 23
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 35
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => 25
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0] => 24
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 22
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 22
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 22
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 33
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 25
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 24
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 23
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 21
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 21
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 21
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 21
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 31
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 19
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 32
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 19
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 19
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 31
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 19
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 19
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 19
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 30
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 19
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 19
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 19
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 19
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 29
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 27
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => 27
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 27
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 27
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 27
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 36
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 1
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 12
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 12
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 24
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 23
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 22
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 20
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 20
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 20
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 31
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => 8
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,0,2 1,3,0,5,0,2,2,1 1,4,0,9,0,5,6,5,3,2,4,1,2 1,5,0,14,0,9,13,11,8,8,17,6,14,3,7,5,6,0,4,1 1,6,0,20,0,14,24,19,16,17,41,17,40,14,34,21,33,12,29,13,15,10,12,5,6,5,2,3
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + 2\ q^{3}$
$F_{4} = 1 + 3\ q + 5\ q^{3} + 2\ q^{5} + 2\ q^{6} + q^{7}$
$F_{5} = 1 + 4\ q + 9\ q^{3} + 5\ q^{5} + 6\ q^{6} + 5\ q^{7} + 3\ q^{8} + 2\ q^{9} + 4\ q^{10} + q^{11} + 2\ q^{12}$
$F_{6} = 1 + 5\ q + 14\ q^{3} + 9\ q^{5} + 13\ q^{6} + 11\ q^{7} + 8\ q^{8} + 8\ q^{9} + 17\ q^{10} + 6\ q^{11} + 14\ q^{12} + 3\ q^{13} + 7\ q^{14} + 5\ q^{15} + 6\ q^{16} + 4\ q^{18} + q^{19}$
$F_{7} = 1 + 6\ q + 20\ q^{3} + 14\ q^{5} + 24\ q^{6} + 19\ q^{7} + 16\ q^{8} + 17\ q^{9} + 41\ q^{10} + 17\ q^{11} + 40\ q^{12} + 14\ q^{13} + 34\ q^{14} + 21\ q^{15} + 33\ q^{16} + 12\ q^{17} + 29\ q^{18} + 13\ q^{19} + 15\ q^{20} + 10\ q^{21} + 12\ q^{22} + 5\ q^{23} + 6\ q^{24} + 5\ q^{25} + 2\ q^{26} + 3\ q^{27}$
Description
The sum of the positions of double up-steps of a Dyck path.
This is part of MacMahon's equal index of a word, see [1, p. 135].
This is part of MacMahon's equal index of a word, see [1, p. 135].
References
[1] MacMahon, P. A. Combinatory analysis. Vol. I, II (bound in one volume) MathSciNet:2417935
Code
def statistic(p):
return sum( i+1 for i in range(len(p)-1) if p[i] == p[i+1] == 1 )
Created
Sep 08, 2017 at 12:18 by Christian Stump
Updated
Sep 08, 2017 at 12:18 by Christian Stump
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!