Identifier
- St001348: Dyck paths ⟶ ℤ
Values
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 2
[1,0,1,0,1,0] => 3
[1,0,1,1,0,0] => 4
[1,1,0,0,1,0] => 3
[1,1,0,1,0,0] => 3
[1,1,1,0,0,0] => 3
[1,0,1,0,1,0,1,0] => 4
[1,0,1,0,1,1,0,0] => 5
[1,0,1,1,0,0,1,0] => 6
[1,0,1,1,0,1,0,0] => 6
[1,0,1,1,1,0,0,0] => 5
[1,1,0,0,1,0,1,0] => 4
[1,1,0,0,1,1,0,0] => 5
[1,1,0,1,0,0,1,0] => 4
[1,1,0,1,0,1,0,0] => 4
[1,1,0,1,1,0,0,0] => 4
[1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,0] => 5
[1,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,0] => 4
[1,0,1,0,1,0,1,0,1,0] => 5
[1,0,1,0,1,0,1,1,0,0] => 6
[1,0,1,0,1,1,0,0,1,0] => 7
[1,0,1,0,1,1,0,1,0,0] => 7
[1,0,1,0,1,1,1,0,0,0] => 6
[1,0,1,1,0,0,1,0,1,0] => 8
[1,0,1,1,0,0,1,1,0,0] => 9
[1,0,1,1,0,1,0,0,1,0] => 8
[1,0,1,1,0,1,0,1,0,0] => 8
[1,0,1,1,0,1,1,0,0,0] => 8
[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] => 6
[1,0,1,1,1,1,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0] => 5
[1,1,0,0,1,0,1,1,0,0] => 6
[1,1,0,0,1,1,0,0,1,0] => 7
[1,1,0,0,1,1,0,1,0,0] => 7
[1,1,0,0,1,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,0,1,0] => 5
[1,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,0] => 5
[1,1,0,1,0,1,0,1,0,0] => 5
[1,1,0,1,0,1,1,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0] => 5
[1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,1,0,1,0,0,0] => 5
[1,1,0,1,1,1,0,0,0,0] => 5
[1,1,1,0,0,0,1,0,1,0] => 5
[1,1,1,0,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,0] => 7
[1,1,1,0,0,1,0,1,0,0] => 7
[1,1,1,0,0,1,1,0,0,0] => 6
[1,1,1,0,1,0,0,0,1,0] => 5
[1,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,0] => 5
[1,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0] => 6
[1,1,1,1,0,0,1,0,0,0] => 5
[1,1,1,1,0,1,0,0,0,0] => 5
[1,1,1,1,1,0,0,0,0,0] => 5
[1,0,1,0,1,0,1,0,1,0,1,0] => 6
[1,0,1,0,1,0,1,0,1,1,0,0] => 7
[1,0,1,0,1,0,1,1,0,0,1,0] => 8
[1,0,1,0,1,0,1,1,0,1,0,0] => 8
[1,0,1,0,1,0,1,1,1,0,0,0] => 7
[1,0,1,0,1,1,0,0,1,0,1,0] => 9
[1,0,1,0,1,1,0,0,1,1,0,0] => 10
[1,0,1,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,0,1,1,0,1,0,1,0,0] => 9
[1,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,0,0,1,0] => 8
[1,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0] => 7
[1,0,1,0,1,1,1,1,0,0,0,0] => 8
[1,0,1,1,0,0,1,0,1,0,1,0] => 10
[1,0,1,1,0,0,1,0,1,1,0,0] => 11
[1,0,1,1,0,0,1,1,0,0,1,0] => 12
[1,0,1,1,0,0,1,1,0,1,0,0] => 12
[1,0,1,1,0,0,1,1,1,0,0,0] => 11
[1,0,1,1,0,1,0,0,1,0,1,0] => 10
[1,0,1,1,0,1,0,0,1,1,0,0] => 11
[1,0,1,1,0,1,0,1,0,0,1,0] => 10
[1,0,1,1,0,1,0,1,0,1,0,0] => 10
[1,0,1,1,0,1,0,1,1,0,0,0] => 10
[1,0,1,1,0,1,1,0,0,0,1,0] => 10
[1,0,1,1,0,1,1,0,0,1,0,0] => 11
[1,0,1,1,0,1,1,0,1,0,0,0] => 10
[1,0,1,1,0,1,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,0,0,1,0,1,0] => 9
[1,0,1,1,1,0,0,0,1,1,0,0] => 10
[1,0,1,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,1,0,0,1,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,0,0,1,0] => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => 8
[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] => 8
>>> Load all 1200 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => 9
[1,0,1,1,1,1,0,0,0,1,0,0] => 9
[1,0,1,1,1,1,0,0,1,0,0,0] => 9
[1,0,1,1,1,1,0,1,0,0,0,0] => 9
[1,0,1,1,1,1,1,0,0,0,0,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0] => 6
[1,1,0,0,1,0,1,0,1,1,0,0] => 7
[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] => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => 9
[1,1,0,0,1,1,0,0,1,1,0,0] => 10
[1,1,0,0,1,1,0,1,0,0,1,0] => 9
[1,1,0,0,1,1,0,1,0,1,0,0] => 9
[1,1,0,0,1,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,0,0,1,0] => 8
[1,1,0,0,1,1,1,0,0,1,0,0] => 8
[1,1,0,0,1,1,1,0,1,0,0,0] => 7
[1,1,0,0,1,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,0,1,1,0,0] => 7
[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] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,1,0,0,1,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => 6
[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] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,1,1,0,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,0,1,1,0,0] => 7
[1,1,0,1,1,0,0,1,0,0,1,0] => 8
[1,1,0,1,1,0,0,1,0,1,0,0] => 8
[1,1,0,1,1,0,0,1,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,0] => 6
[1,1,0,1,1,0,1,0,0,1,0,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,0,0,0] => 7
[1,1,0,1,1,1,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,0,0,0,1,0,0] => 7
[1,1,0,1,1,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,1,0,1,0,0,0,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,0] => 6
[1,1,1,0,0,0,1,0,1,0,1,0] => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => 7
[1,1,1,0,0,0,1,1,0,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,1,0,0] => 8
[1,1,1,0,0,0,1,1,1,0,0,0] => 7
[1,1,1,0,0,1,0,0,1,0,1,0] => 9
[1,1,1,0,0,1,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,0] => 9
[1,1,1,0,0,1,0,1,1,0,0,0] => 9
[1,1,1,0,0,1,1,0,0,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,1,0,0] => 8
[1,1,1,0,0,1,1,0,1,0,0,0] => 7
[1,1,1,0,0,1,1,1,0,0,0,0] => 8
[1,1,1,0,1,0,0,0,1,0,1,0] => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => 7
[1,1,1,0,1,0,0,1,0,0,1,0] => 8
[1,1,1,0,1,0,0,1,0,1,0,0] => 8
[1,1,1,0,1,0,0,1,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,0] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => 7
[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] => 7
[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] => 7
[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] => 8
[1,1,1,1,0,0,0,1,0,1,0,0] => 8
[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] => 6
[1,1,1,1,0,0,1,0,0,1,0,0] => 7
[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] => 7
[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] => 7
[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] => 6
[1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => 7
[1,1,1,1,1,0,0,0,1,0,0,0] => 6
[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] => 6
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 8
[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] => 8
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 10
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 11
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 13
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 12
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 11
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 11
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 11
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 11
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 12
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 11
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 10
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 12
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 16
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 15
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 15
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 15
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 14
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 14
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 13
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 12
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 13
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 13
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 12
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 12
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 13
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 13
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 14
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 14
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 13
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 13
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 13
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 13
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 12
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 11
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 12
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 13
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 12
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 11
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 12
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 11
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 11
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 12
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 11
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 11
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 9
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 11
[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] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 11
[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] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 9
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 10
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 10
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 8
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 11
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 13
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 13
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 12
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 11
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 11
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 11
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 11
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 10
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 11
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 10
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 9
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 9
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 10
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 11
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 10
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 10
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 8
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 8
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 7
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 7
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 7
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 7
[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] => 8
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 8
[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] => 8
[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] => 8
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 7
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 8
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 7
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 7
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 7
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 8
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 10
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 11
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 10
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 10
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 9
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 9
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 9
[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] => 7
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 8
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 9
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 9
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 8
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 7
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 7
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 7
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 7
[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] => 7
[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] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 7
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 8
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 9
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 9
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 8
[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] => 11
[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] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 9
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 9
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 8
[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] => 11
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 13
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 13
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 12
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 11
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 11
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 11
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 11
[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] => 12
[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] => 11
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 10
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 11
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 10
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 10
[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] => 8
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 10
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 10
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 10
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 10
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 8
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 9
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 11
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 9
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 9
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 8
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 7
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 8
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 9
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 9
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 11
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 10
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 10
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 9
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 9
[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] => 9
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 10
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 10
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 9
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 9
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 9
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 8
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 9
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 7
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 8
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 9
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 9
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 10
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 11
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 10
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 10
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 9
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 9
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 8
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 8
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 7
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 9
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 9
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 8
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 9
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 8
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 9
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 9
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 7
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 7
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 8
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 7
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 7
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 7
[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] => 8
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 8
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 7
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 7
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 8
[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] => 8
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 7
[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] => 8
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 9
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 9
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 8
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 9
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 8
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 7
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 8
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 7
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 7
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 11
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 11
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 10
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 13
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 14
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 13
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 12
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 13
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 10
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 11
[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] => 13
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 15
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 15
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 16
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 17
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 16
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 16
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 14
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 15
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 15
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 14
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 13
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 13
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 14
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 13
[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] => 14
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 15
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 14
[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] => 14
[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] => 14
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 14
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 13
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 12
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 13
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 13
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 12
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 12
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 12
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 12
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 13
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 12
[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] => 12
[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] => 11
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 13
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 13
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 12
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 11
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 14
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 16
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 17
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 18
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 17
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 17
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 17
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 16
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 16
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 15
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 16
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 20
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 20
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 19
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 19
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 18
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 19
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 17
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 16
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 16
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 15
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 16
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 17
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 17
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 17
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 17
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 16
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 14
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 16
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 17
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 17
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 17
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 17
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 16
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 16
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 16
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 14
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 14
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 15
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 14
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 14
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 15
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 16
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 16
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 15
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 15
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 15
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 14
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 15
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 14
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 14
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 15
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 17
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 18
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 17
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 17
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 17
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 14
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 15
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 15
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 14
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 16
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 16
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 15
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 16
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 14
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 15
[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] => 15
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 15
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 14
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 15
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 14
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 14
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 15
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 14
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 15
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 14
[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] => 13
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 15
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 14
[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] => 17
[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] => 16
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 15
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 15
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 14
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 15
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 15
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 14
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 13
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 14
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 13
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 13
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 13
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 14
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 13
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 13
[1,0,1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 14
[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] => 14
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 13
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 12
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 13
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 14
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 14
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 13
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 12
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 13
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 12
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 10
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 9
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 10
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 13
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 13
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 11
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 10
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 11
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 14
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 15
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 15
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 14
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 14
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 13
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 13
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 14
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 15
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 15
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 14
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 14
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 14
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 13
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 13
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 11
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 10
[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] => 12
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 12
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 12
[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] => 12
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 12
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 11
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 11
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => 11
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => 11
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => 11
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0] => 10
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => 10
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => 13
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => 14
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0] => 14
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 13
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0] => 13
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => 12
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => 13
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0] => 12
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 12
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 13
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => 15
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => 16
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 17
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => 16
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => 16
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => 16
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 15
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => 15
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => 14
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0] => 13
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0] => 14
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0] => 15
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0] => 15
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => 14
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0] => 13
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => 14
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => 13
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => 13
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0] => 13
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0] => 13
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => 14
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0] => 13
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => 13
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => 13
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0] => 15
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0] => 15
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => 14
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => 13
[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] => 13
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => 14
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0] => 13
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0] => 14
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0] => 13
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0] => 13
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => 13
[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] => 13
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 14
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0] => 14
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 13
[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] => 13
[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] => 12
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0] => 13
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => 12
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => 9
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => 13
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => 12
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => 12
[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] => 11
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => 11
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => 11
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 11
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => 8
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => 10
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => 11
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => 12
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0] => 11
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => 11
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => 11
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0] => 10
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => 10
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => 10
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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:
4,1 8,4,2 16,12,9,4,1 32,32,30,20,12,4,2 64,80,88,73,56,34,20,9,4,1
$F_{1} = q$
$F_{2} = 2\ q^{2}$
$F_{3} = 4\ q^{3} + q^{4}$
$F_{4} = 8\ q^{4} + 4\ q^{5} + 2\ q^{6}$
$F_{5} = 16\ q^{5} + 12\ q^{6} + 9\ q^{7} + 4\ q^{8} + q^{9}$
$F_{6} = 32\ q^{6} + 32\ q^{7} + 30\ q^{8} + 20\ q^{9} + 12\ q^{10} + 4\ q^{11} + 2\ q^{12}$
$F_{7} = 64\ q^{7} + 80\ q^{8} + 88\ q^{9} + 73\ q^{10} + 56\ q^{11} + 34\ q^{12} + 20\ q^{13} + 9\ q^{14} + 4\ q^{15} + q^{16}$
Description
The bounce of the parallelogram polyomino associated with the Dyck path.
A bijection due to Delest and Viennot [1] associates a Dyck path with a parallelogram polyomino. The bounce statistic is defined in [2].
A bijection due to Delest and Viennot [1] associates a Dyck path with a parallelogram polyomino. The bounce statistic is defined in [2].
References
[1] Delest, M.-P., Viennot, Gérard Algebraic languages and polyominoes enumeration MathSciNet:0774044
[2] Aval, J.-C., D'Adderio, M., Dukes, M., Hicks, A., Le Borgne, Y. Statistics on parallelogram polyominoes and a q,t-analogue of the Narayana numbers arXiv:1301.4803
[2] Aval, J.-C., D'Adderio, M., Dukes, M., Hicks, A., Le Borgne, Y. Statistics on parallelogram polyominoes and a q,t-analogue of the Narayana numbers arXiv:1301.4803
Code
def statistic(D):
return ParallelogramPolyomino.from_dyck_word(D).bounce()
Created
Jan 26, 2019 at 16:12 by Martin Rubey
Updated
Jan 26, 2019 at 16:12 by Martin Rubey
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