Identifier
Values
[1] => 0
[2] => 1
[1,1] => 0
[3] => 2
[2,1] => 0
[1,1,1] => 0
[4] => 3
[3,1] => 2
[2,2] => 1
[2,1,1] => 0
[1,1,1,1] => 0
[5] => 4
[4,1] => 3
[3,2] => 1
[3,1,1] => 2
[2,2,1] => 0
[2,1,1,1] => 0
[1,1,1,1,1] => 0
[6] => 5
[5,1] => 4
[4,2] => 3
[4,1,1] => 3
[3,3] => 2
[3,2,1] => 0
[3,1,1,1] => 2
[2,2,2] => 1
[2,2,1,1] => 0
[2,1,1,1,1] => 0
[1,1,1,1,1,1] => 0
[7] => 6
[6,1] => 5
[5,2] => 4
[5,1,1] => 4
[4,3] => 2
[4,2,1] => 3
[4,1,1,1] => 3
[3,3,1] => 2
[3,2,2] => 1
[3,2,1,1] => 0
[3,1,1,1,1] => 2
[2,2,2,1] => 0
[2,2,1,1,1] => 0
[2,1,1,1,1,1] => 0
[1,1,1,1,1,1,1] => 0
[8] => 7
[7,1] => 6
[6,2] => 5
[6,1,1] => 5
[5,3] => 4
[5,2,1] => 4
[5,1,1,1] => 4
[4,4] => 3
[4,3,1] => 2
[4,2,2] => 3
[4,2,1,1] => 3
[4,1,1,1,1] => 3
[3,3,2] => 1
[3,3,1,1] => 2
[3,2,2,1] => 0
[3,2,1,1,1] => 0
[3,1,1,1,1,1] => 2
[2,2,2,2] => 1
[2,2,2,1,1] => 0
[2,2,1,1,1,1] => 0
[2,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1] => 0
[9] => 8
[8,1] => 7
[7,2] => 6
[7,1,1] => 6
[6,3] => 5
[6,2,1] => 5
[6,1,1,1] => 5
[5,4] => 3
[5,3,1] => 4
[5,2,2] => 4
[5,2,1,1] => 4
[5,1,1,1,1] => 4
[4,4,1] => 3
[4,3,2] => 1
[4,3,1,1] => 2
[4,2,2,1] => 3
[4,2,1,1,1] => 3
[4,1,1,1,1,1] => 3
[3,3,3] => 2
[3,3,2,1] => 0
[3,3,1,1,1] => 2
[3,2,2,2] => 1
[3,2,2,1,1] => 0
[3,2,1,1,1,1] => 0
[3,1,1,1,1,1,1] => 2
[2,2,2,2,1] => 0
[2,2,2,1,1,1] => 0
[2,2,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1] => 0
[10] => 9
[9,1] => 8
[8,2] => 7
[8,1,1] => 7
[7,3] => 6
>>> Load all 1200 entries. <<<[7,2,1] => 6
[7,1,1,1] => 6
[6,4] => 5
[6,3,1] => 5
[6,2,2] => 5
[6,2,1,1] => 5
[6,1,1,1,1] => 5
[5,5] => 4
[5,4,1] => 3
[5,3,2] => 4
[5,3,1,1] => 4
[5,2,2,1] => 4
[5,2,1,1,1] => 4
[5,1,1,1,1,1] => 4
[4,4,2] => 3
[4,4,1,1] => 3
[4,3,3] => 2
[4,3,2,1] => 0
[4,3,1,1,1] => 2
[4,2,2,2] => 3
[4,2,2,1,1] => 3
[4,2,1,1,1,1] => 3
[4,1,1,1,1,1,1] => 3
[3,3,3,1] => 2
[3,3,2,2] => 1
[3,3,2,1,1] => 0
[3,3,1,1,1,1] => 2
[3,2,2,2,1] => 0
[3,2,2,1,1,1] => 0
[3,2,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1] => 2
[2,2,2,2,2] => 1
[2,2,2,2,1,1] => 0
[2,2,2,1,1,1,1] => 0
[2,2,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 10
[10,1] => 9
[9,2] => 8
[9,1,1] => 8
[8,3] => 7
[8,2,1] => 7
[8,1,1,1] => 7
[7,4] => 6
[7,3,1] => 6
[7,2,2] => 6
[7,2,1,1] => 6
[7,1,1,1,1] => 6
[6,5] => 4
[6,4,1] => 5
[6,3,2] => 5
[6,3,1,1] => 5
[6,2,2,1] => 5
[6,2,1,1,1] => 5
[6,1,1,1,1,1] => 5
[5,5,1] => 4
[5,4,2] => 3
[5,4,1,1] => 3
[5,3,3] => 4
[5,3,2,1] => 4
[5,3,1,1,1] => 4
[5,2,2,2] => 4
[5,2,2,1,1] => 4
[5,2,1,1,1,1] => 4
[5,1,1,1,1,1,1] => 4
[4,4,3] => 2
[4,4,2,1] => 3
[4,4,1,1,1] => 3
[4,3,3,1] => 2
[4,3,2,2] => 1
[4,3,2,1,1] => 0
[4,3,1,1,1,1] => 2
[4,2,2,2,1] => 3
[4,2,2,1,1,1] => 3
[4,2,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1] => 3
[3,3,3,2] => 1
[3,3,3,1,1] => 2
[3,3,2,2,1] => 0
[3,3,2,1,1,1] => 0
[3,3,1,1,1,1,1] => 2
[3,2,2,2,2] => 1
[3,2,2,2,1,1] => 0
[3,2,2,1,1,1,1] => 0
[3,2,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,1] => 0
[2,2,2,2,1,1,1] => 0
[2,2,2,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 11
[11,1] => 10
[10,2] => 9
[10,1,1] => 9
[9,3] => 8
[9,2,1] => 8
[9,1,1,1] => 8
[8,4] => 7
[8,3,1] => 7
[8,2,2] => 7
[8,2,1,1] => 7
[8,1,1,1,1] => 7
[7,5] => 6
[7,4,1] => 6
[7,3,2] => 6
[7,3,1,1] => 6
[7,2,2,1] => 6
[7,2,1,1,1] => 6
[7,1,1,1,1,1] => 6
[6,6] => 5
[6,5,1] => 4
[6,4,2] => 5
[6,4,1,1] => 5
[6,3,3] => 5
[6,3,2,1] => 5
[6,3,1,1,1] => 5
[6,2,2,2] => 5
[6,2,2,1,1] => 5
[6,2,1,1,1,1] => 5
[6,1,1,1,1,1,1] => 5
[5,5,2] => 4
[5,5,1,1] => 4
[5,4,3] => 2
[5,4,2,1] => 3
[5,4,1,1,1] => 3
[5,3,3,1] => 4
[5,3,2,2] => 4
[5,3,2,1,1] => 4
[5,3,1,1,1,1] => 4
[5,2,2,2,1] => 4
[5,2,2,1,1,1] => 4
[5,2,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1] => 4
[4,4,4] => 3
[4,4,3,1] => 2
[4,4,2,2] => 3
[4,4,2,1,1] => 3
[4,4,1,1,1,1] => 3
[4,3,3,2] => 1
[4,3,3,1,1] => 2
[4,3,2,2,1] => 0
[4,3,2,1,1,1] => 0
[4,3,1,1,1,1,1] => 2
[4,2,2,2,2] => 3
[4,2,2,2,1,1] => 3
[4,2,2,1,1,1,1] => 3
[4,2,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1] => 3
[3,3,3,3] => 2
[3,3,3,2,1] => 0
[3,3,3,1,1,1] => 2
[3,3,2,2,2] => 1
[3,3,2,2,1,1] => 0
[3,3,2,1,1,1,1] => 0
[3,3,1,1,1,1,1,1] => 2
[3,2,2,2,2,1] => 0
[3,2,2,2,1,1,1] => 0
[3,2,2,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2] => 1
[2,2,2,2,2,1,1] => 0
[2,2,2,2,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 12
[12,1] => 11
[11,2] => 10
[11,1,1] => 10
[10,3] => 9
[10,2,1] => 9
[10,1,1,1] => 9
[9,4] => 8
[9,3,1] => 8
[9,2,2] => 8
[9,2,1,1] => 8
[9,1,1,1,1] => 8
[8,5] => 7
[8,4,1] => 7
[8,3,2] => 7
[8,3,1,1] => 7
[8,2,2,1] => 7
[8,2,1,1,1] => 7
[8,1,1,1,1,1] => 7
[7,6] => 5
[7,5,1] => 6
[7,4,2] => 6
[7,4,1,1] => 6
[7,3,3] => 6
[7,3,2,1] => 6
[7,3,1,1,1] => 6
[7,2,2,2] => 6
[7,2,2,1,1] => 6
[7,2,1,1,1,1] => 6
[7,1,1,1,1,1,1] => 6
[6,6,1] => 5
[6,5,2] => 4
[6,5,1,1] => 4
[6,4,3] => 5
[6,4,2,1] => 5
[6,4,1,1,1] => 5
[6,3,3,1] => 5
[6,3,2,2] => 5
[6,3,2,1,1] => 5
[6,3,1,1,1,1] => 5
[6,2,2,2,1] => 5
[6,2,2,1,1,1] => 5
[6,2,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1] => 5
[5,5,3] => 4
[5,5,2,1] => 4
[5,5,1,1,1] => 4
[5,4,4] => 3
[5,4,3,1] => 2
[5,4,2,2] => 3
[5,4,2,1,1] => 3
[5,4,1,1,1,1] => 3
[5,3,3,2] => 4
[5,3,3,1,1] => 4
[5,3,2,2,1] => 4
[5,3,2,1,1,1] => 4
[5,3,1,1,1,1,1] => 4
[5,2,2,2,2] => 4
[5,2,2,2,1,1] => 4
[5,2,2,1,1,1,1] => 4
[5,2,1,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1,1] => 4
[4,4,4,1] => 3
[4,4,3,2] => 1
[4,4,3,1,1] => 2
[4,4,2,2,1] => 3
[4,4,2,1,1,1] => 3
[4,4,1,1,1,1,1] => 3
[4,3,3,3] => 2
[4,3,3,2,1] => 0
[4,3,3,1,1,1] => 2
[4,3,2,2,2] => 1
[4,3,2,2,1,1] => 0
[4,3,2,1,1,1,1] => 0
[4,3,1,1,1,1,1,1] => 2
[4,2,2,2,2,1] => 3
[4,2,2,2,1,1,1] => 3
[4,2,2,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,1] => 2
[3,3,3,2,2] => 1
[3,3,3,2,1,1] => 0
[3,3,3,1,1,1,1] => 2
[3,3,2,2,2,1] => 0
[3,3,2,2,1,1,1] => 0
[3,3,2,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2] => 1
[3,2,2,2,2,1,1] => 0
[3,2,2,2,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,1] => 0
[2,2,2,2,2,1,1,1] => 0
[2,2,2,2,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => 13
[13,1] => 12
[12,2] => 11
[12,1,1] => 11
[11,3] => 10
[11,2,1] => 10
[11,1,1,1] => 10
[10,4] => 9
[10,3,1] => 9
[10,2,2] => 9
[10,2,1,1] => 9
[10,1,1,1,1] => 9
[9,5] => 8
[9,4,1] => 8
[9,3,2] => 8
[9,3,1,1] => 8
[9,2,2,1] => 8
[9,2,1,1,1] => 8
[9,1,1,1,1,1] => 8
[8,6] => 7
[8,5,1] => 7
[8,4,2] => 7
[8,4,1,1] => 7
[8,3,3] => 7
[8,3,2,1] => 7
[8,3,1,1,1] => 7
[8,2,2,2] => 7
[8,2,2,1,1] => 7
[8,2,1,1,1,1] => 7
[8,1,1,1,1,1,1] => 7
[7,7] => 6
[7,6,1] => 5
[7,5,2] => 6
[7,5,1,1] => 6
[7,4,3] => 6
[7,4,2,1] => 6
[7,4,1,1,1] => 6
[7,3,3,1] => 6
[7,3,2,2] => 6
[7,3,2,1,1] => 6
[7,3,1,1,1,1] => 6
[7,2,2,2,1] => 6
[7,2,2,1,1,1] => 6
[7,2,1,1,1,1,1] => 6
[7,1,1,1,1,1,1,1] => 6
[6,6,2] => 5
[6,6,1,1] => 5
[6,5,3] => 4
[6,5,2,1] => 4
[6,5,1,1,1] => 4
[6,4,4] => 5
[6,4,3,1] => 5
[6,4,2,2] => 5
[6,4,2,1,1] => 5
[6,4,1,1,1,1] => 5
[6,3,3,2] => 5
[6,3,3,1,1] => 5
[6,3,2,2,1] => 5
[6,3,2,1,1,1] => 5
[6,3,1,1,1,1,1] => 5
[6,2,2,2,2] => 5
[6,2,2,2,1,1] => 5
[6,2,2,1,1,1,1] => 5
[6,2,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1] => 5
[5,5,4] => 3
[5,5,3,1] => 4
[5,5,2,2] => 4
[5,5,2,1,1] => 4
[5,5,1,1,1,1] => 4
[5,4,4,1] => 3
[5,4,3,2] => 1
[5,4,3,1,1] => 2
[5,4,2,2,1] => 3
[5,4,2,1,1,1] => 3
[5,4,1,1,1,1,1] => 3
[5,3,3,3] => 4
[5,3,3,2,1] => 4
[5,3,3,1,1,1] => 4
[5,3,2,2,2] => 4
[5,3,2,2,1,1] => 4
[5,3,2,1,1,1,1] => 4
[5,3,1,1,1,1,1,1] => 4
[5,2,2,2,2,1] => 4
[5,2,2,2,1,1,1] => 4
[5,2,2,1,1,1,1,1] => 4
[5,2,1,1,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,2] => 3
[4,4,4,1,1] => 3
[4,4,3,3] => 2
[4,4,3,2,1] => 0
[4,4,3,1,1,1] => 2
[4,4,2,2,2] => 3
[4,4,2,2,1,1] => 3
[4,4,2,1,1,1,1] => 3
[4,4,1,1,1,1,1,1] => 3
[4,3,3,3,1] => 2
[4,3,3,2,2] => 1
[4,3,3,2,1,1] => 0
[4,3,3,1,1,1,1] => 2
[4,3,2,2,2,1] => 0
[4,3,2,2,1,1,1] => 0
[4,3,2,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1] => 2
[4,2,2,2,2,2] => 3
[4,2,2,2,2,1,1] => 3
[4,2,2,2,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,2] => 1
[3,3,3,3,1,1] => 2
[3,3,3,2,2,1] => 0
[3,3,3,2,1,1,1] => 0
[3,3,3,1,1,1,1,1] => 2
[3,3,2,2,2,2] => 1
[3,3,2,2,2,1,1] => 0
[3,3,2,2,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,1] => 0
[3,2,2,2,2,1,1,1] => 0
[3,2,2,2,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,2] => 1
[2,2,2,2,2,2,1,1] => 0
[2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 14
[14,1] => 13
[13,2] => 12
[13,1,1] => 12
[12,3] => 11
[12,2,1] => 11
[12,1,1,1] => 11
[11,4] => 10
[11,3,1] => 10
[11,2,2] => 10
[11,2,1,1] => 10
[11,1,1,1,1] => 10
[10,5] => 9
[10,4,1] => 9
[10,3,2] => 9
[10,3,1,1] => 9
[10,2,2,1] => 9
[10,2,1,1,1] => 9
[10,1,1,1,1,1] => 9
[9,6] => 8
[9,5,1] => 8
[9,4,2] => 8
[9,4,1,1] => 8
[9,3,3] => 8
[9,3,2,1] => 8
[9,3,1,1,1] => 8
[9,2,2,2] => 8
[9,2,2,1,1] => 8
[9,2,1,1,1,1] => 8
[9,1,1,1,1,1,1] => 8
[8,7] => 6
[8,6,1] => 7
[8,5,2] => 7
[8,5,1,1] => 7
[8,4,3] => 7
[8,4,2,1] => 7
[8,4,1,1,1] => 7
[8,3,3,1] => 7
[8,3,2,2] => 7
[8,3,2,1,1] => 7
[8,3,1,1,1,1] => 7
[8,2,2,2,1] => 7
[8,2,2,1,1,1] => 7
[8,2,1,1,1,1,1] => 7
[8,1,1,1,1,1,1,1] => 7
[7,7,1] => 6
[7,6,2] => 5
[7,6,1,1] => 5
[7,5,3] => 6
[7,5,2,1] => 6
[7,5,1,1,1] => 6
[7,4,4] => 6
[7,4,3,1] => 6
[7,4,2,2] => 6
[7,4,2,1,1] => 6
[7,4,1,1,1,1] => 6
[7,3,3,2] => 6
[7,3,3,1,1] => 6
[7,3,2,2,1] => 6
[7,3,2,1,1,1] => 6
[7,3,1,1,1,1,1] => 6
[7,2,2,2,2] => 6
[7,2,2,2,1,1] => 6
[7,2,2,1,1,1,1] => 6
[7,2,1,1,1,1,1,1] => 6
[7,1,1,1,1,1,1,1,1] => 6
[6,6,3] => 5
[6,6,2,1] => 5
[6,6,1,1,1] => 5
[6,5,4] => 3
[6,5,3,1] => 4
[6,5,2,2] => 4
[6,5,2,1,1] => 4
[6,5,1,1,1,1] => 4
[6,4,4,1] => 5
[6,4,3,2] => 5
[6,4,3,1,1] => 5
[6,4,2,2,1] => 5
[6,4,2,1,1,1] => 5
[6,4,1,1,1,1,1] => 5
[6,3,3,3] => 5
[6,3,3,2,1] => 5
[6,3,3,1,1,1] => 5
[6,3,2,2,2] => 5
[6,3,2,2,1,1] => 5
[6,3,2,1,1,1,1] => 5
[6,3,1,1,1,1,1,1] => 5
[6,2,2,2,2,1] => 5
[6,2,2,2,1,1,1] => 5
[6,2,2,1,1,1,1,1] => 5
[6,2,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1] => 5
[5,5,5] => 4
[5,5,4,1] => 3
[5,5,3,2] => 4
[5,5,3,1,1] => 4
[5,5,2,2,1] => 4
[5,5,2,1,1,1] => 4
[5,5,1,1,1,1,1] => 4
[5,4,4,2] => 3
[5,4,4,1,1] => 3
[5,4,3,3] => 2
[5,4,3,2,1] => 0
[5,4,3,1,1,1] => 2
[5,4,2,2,2] => 3
[5,4,2,2,1,1] => 3
[5,4,2,1,1,1,1] => 3
[5,4,1,1,1,1,1,1] => 3
[5,3,3,3,1] => 4
[5,3,3,2,2] => 4
[5,3,3,2,1,1] => 4
[5,3,3,1,1,1,1] => 4
[5,3,2,2,2,1] => 4
[5,3,2,2,1,1,1] => 4
[5,3,2,1,1,1,1,1] => 4
[5,3,1,1,1,1,1,1,1] => 4
[5,2,2,2,2,2] => 4
[5,2,2,2,2,1,1] => 4
[5,2,2,2,1,1,1,1] => 4
[5,2,2,1,1,1,1,1,1] => 4
[5,2,1,1,1,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,3] => 2
[4,4,4,2,1] => 3
[4,4,4,1,1,1] => 3
[4,4,3,3,1] => 2
[4,4,3,2,2] => 1
[4,4,3,2,1,1] => 0
[4,4,3,1,1,1,1] => 2
[4,4,2,2,2,1] => 3
[4,4,2,2,1,1,1] => 3
[4,4,2,1,1,1,1,1] => 3
[4,4,1,1,1,1,1,1,1] => 3
[4,3,3,3,2] => 1
[4,3,3,3,1,1] => 2
[4,3,3,2,2,1] => 0
[4,3,3,2,1,1,1] => 0
[4,3,3,1,1,1,1,1] => 2
[4,3,2,2,2,2] => 1
[4,3,2,2,2,1,1] => 0
[4,3,2,2,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1] => 2
[4,2,2,2,2,2,1] => 3
[4,2,2,2,2,1,1,1] => 3
[4,2,2,2,1,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3] => 2
[3,3,3,3,2,1] => 0
[3,3,3,3,1,1,1] => 2
[3,3,3,2,2,2] => 1
[3,3,3,2,2,1,1] => 0
[3,3,3,2,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1] => 2
[3,3,2,2,2,2,1] => 0
[3,3,2,2,2,1,1,1] => 0
[3,3,2,2,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,2] => 1
[3,2,2,2,2,2,1,1] => 0
[3,2,2,2,2,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,2,1] => 0
[2,2,2,2,2,2,1,1,1] => 0
[2,2,2,2,2,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[16] => 15
[15,1] => 14
[14,2] => 13
[14,1,1] => 13
[13,3] => 12
[13,2,1] => 12
[13,1,1,1] => 12
[12,4] => 11
[12,3,1] => 11
[12,2,2] => 11
[12,2,1,1] => 11
[12,1,1,1,1] => 11
[11,5] => 10
[11,4,1] => 10
[11,3,2] => 10
[11,3,1,1] => 10
[11,2,2,1] => 10
[11,2,1,1,1] => 10
[11,1,1,1,1,1] => 10
[10,6] => 9
[10,5,1] => 9
[10,4,2] => 9
[10,4,1,1] => 9
[10,3,3] => 9
[10,3,2,1] => 9
[10,3,1,1,1] => 9
[10,2,2,2] => 9
[10,2,2,1,1] => 9
[10,2,1,1,1,1] => 9
[10,1,1,1,1,1,1] => 9
[9,7] => 8
[9,6,1] => 8
[9,5,2] => 8
[9,5,1,1] => 8
[9,4,3] => 8
[9,4,2,1] => 8
[9,4,1,1,1] => 8
[9,3,3,1] => 8
[9,3,2,2] => 8
[9,3,2,1,1] => 8
[9,3,1,1,1,1] => 8
[9,2,2,2,1] => 8
[9,2,2,1,1,1] => 8
[9,2,1,1,1,1,1] => 8
[9,1,1,1,1,1,1,1] => 8
[8,8] => 7
[8,7,1] => 6
[8,6,2] => 7
[8,6,1,1] => 7
[8,5,3] => 7
[8,5,2,1] => 7
[8,5,1,1,1] => 7
[8,4,4] => 7
[8,4,3,1] => 7
[8,4,2,2] => 7
[8,4,2,1,1] => 7
[8,4,1,1,1,1] => 7
[8,3,3,2] => 7
[8,3,3,1,1] => 7
[8,3,2,2,1] => 7
[8,3,2,1,1,1] => 7
[8,3,1,1,1,1,1] => 7
[8,2,2,2,2] => 7
[8,2,2,2,1,1] => 7
[8,2,2,1,1,1,1] => 7
[8,2,1,1,1,1,1,1] => 7
[8,1,1,1,1,1,1,1,1] => 7
[7,7,2] => 6
[7,7,1,1] => 6
[7,6,3] => 5
[7,6,2,1] => 5
[7,6,1,1,1] => 5
[7,5,4] => 6
[7,5,3,1] => 6
[7,5,2,2] => 6
[7,5,2,1,1] => 6
[7,5,1,1,1,1] => 6
[7,4,4,1] => 6
[7,4,3,2] => 6
[7,4,3,1,1] => 6
[7,4,2,2,1] => 6
[7,4,2,1,1,1] => 6
[7,4,1,1,1,1,1] => 6
[7,3,3,3] => 6
[7,3,3,2,1] => 6
[7,3,3,1,1,1] => 6
[7,3,2,2,2] => 6
[7,3,2,2,1,1] => 6
[7,3,2,1,1,1,1] => 6
[7,3,1,1,1,1,1,1] => 6
[7,2,2,2,2,1] => 6
[7,2,2,2,1,1,1] => 6
[7,2,2,1,1,1,1,1] => 6
[7,2,1,1,1,1,1,1,1] => 6
[7,1,1,1,1,1,1,1,1,1] => 6
[6,6,4] => 5
[6,6,3,1] => 5
[6,6,2,2] => 5
[6,6,2,1,1] => 5
[6,6,1,1,1,1] => 5
[6,5,5] => 4
[6,5,4,1] => 3
[6,5,3,2] => 4
[6,5,3,1,1] => 4
[6,5,2,2,1] => 4
[6,5,2,1,1,1] => 4
[6,5,1,1,1,1,1] => 4
[6,4,4,2] => 5
[6,4,4,1,1] => 5
[6,4,3,3] => 5
[6,4,3,2,1] => 5
[6,4,3,1,1,1] => 5
[6,4,2,2,2] => 5
[6,4,2,2,1,1] => 5
[6,4,2,1,1,1,1] => 5
[6,4,1,1,1,1,1,1] => 5
[6,3,3,3,1] => 5
[6,3,3,2,2] => 5
[6,3,3,2,1,1] => 5
[6,3,3,1,1,1,1] => 5
[6,3,2,2,2,1] => 5
[6,3,2,2,1,1,1] => 5
[6,3,2,1,1,1,1,1] => 5
[6,3,1,1,1,1,1,1,1] => 5
[6,2,2,2,2,2] => 5
[6,2,2,2,2,1,1] => 5
[6,2,2,2,1,1,1,1] => 5
[6,2,2,1,1,1,1,1,1] => 5
[6,2,1,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1,1] => 5
[5,5,5,1] => 4
[5,5,4,2] => 3
[5,5,4,1,1] => 3
[5,5,3,3] => 4
[5,5,3,2,1] => 4
[5,5,3,1,1,1] => 4
[5,5,2,2,2] => 4
[5,5,2,2,1,1] => 4
[5,5,2,1,1,1,1] => 4
[5,5,1,1,1,1,1,1] => 4
[5,4,4,3] => 2
[5,4,4,2,1] => 3
[5,4,4,1,1,1] => 3
[5,4,3,3,1] => 2
[5,4,3,2,2] => 1
[5,4,3,2,1,1] => 0
[5,4,3,1,1,1,1] => 2
[5,4,2,2,2,1] => 3
[5,4,2,2,1,1,1] => 3
[5,4,2,1,1,1,1,1] => 3
[5,4,1,1,1,1,1,1,1] => 3
[5,3,3,3,2] => 4
[5,3,3,3,1,1] => 4
[5,3,3,2,2,1] => 4
[5,3,3,2,1,1,1] => 4
[5,3,3,1,1,1,1,1] => 4
[5,3,2,2,2,2] => 4
[5,3,2,2,2,1,1] => 4
[5,3,2,2,1,1,1,1] => 4
[5,3,2,1,1,1,1,1,1] => 4
[5,3,1,1,1,1,1,1,1,1] => 4
[5,2,2,2,2,2,1] => 4
[5,2,2,2,2,1,1,1] => 4
[5,2,2,2,1,1,1,1,1] => 4
[5,2,2,1,1,1,1,1,1,1] => 4
[5,2,1,1,1,1,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,4] => 3
[4,4,4,3,1] => 2
[4,4,4,2,2] => 3
[4,4,4,2,1,1] => 3
[4,4,4,1,1,1,1] => 3
[4,4,3,3,2] => 1
[4,4,3,3,1,1] => 2
[4,4,3,2,2,1] => 0
[4,4,3,2,1,1,1] => 0
[4,4,3,1,1,1,1,1] => 2
[4,4,2,2,2,2] => 3
[4,4,2,2,2,1,1] => 3
[4,4,2,2,1,1,1,1] => 3
[4,4,2,1,1,1,1,1,1] => 3
[4,4,1,1,1,1,1,1,1,1] => 3
[4,3,3,3,3] => 2
[4,3,3,3,2,1] => 0
[4,3,3,3,1,1,1] => 2
[4,3,3,2,2,2] => 1
[4,3,3,2,2,1,1] => 0
[4,3,3,2,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1] => 2
[4,3,2,2,2,2,1] => 0
[4,3,2,2,2,1,1,1] => 0
[4,3,2,2,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1] => 2
[4,2,2,2,2,2,2] => 3
[4,2,2,2,2,2,1,1] => 3
[4,2,2,2,2,1,1,1,1] => 3
[4,2,2,2,1,1,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3,1] => 2
[3,3,3,3,2,2] => 1
[3,3,3,3,2,1,1] => 0
[3,3,3,3,1,1,1,1] => 2
[3,3,3,2,2,2,1] => 0
[3,3,3,2,2,1,1,1] => 0
[3,3,3,2,1,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1,1] => 2
[3,3,2,2,2,2,2] => 1
[3,3,2,2,2,2,1,1] => 0
[3,3,2,2,2,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,2,1] => 0
[3,2,2,2,2,2,1,1,1] => 0
[3,2,2,2,2,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1] => 0
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 0
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 2
[2,2,2,2,2,2,2,2] => 1
[2,2,2,2,2,2,2,1,1] => 0
[2,2,2,2,2,2,1,1,1,1] => 0
[2,2,2,2,2,1,1,1,1,1,1] => 0
[2,2,2,2,1,1,1,1,1,1,1,1] => 0
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 0
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 16
[16,1] => 15
[15,2] => 14
[15,1,1] => 14
[14,3] => 13
[14,2,1] => 13
[14,1,1,1] => 13
[13,4] => 12
[13,3,1] => 12
[13,2,2] => 12
[13,2,1,1] => 12
[13,1,1,1,1] => 12
[12,5] => 11
[12,4,1] => 11
[12,3,2] => 11
[12,3,1,1] => 11
[12,2,2,1] => 11
[12,2,1,1,1] => 11
[12,1,1,1,1,1] => 11
[11,6] => 10
[11,5,1] => 10
[11,4,2] => 10
[11,4,1,1] => 10
[11,3,3] => 10
[11,3,2,1] => 10
[11,3,1,1,1] => 10
[11,2,2,2] => 10
[11,2,2,1,1] => 10
[11,2,1,1,1,1] => 10
[11,1,1,1,1,1,1] => 10
[10,7] => 9
[10,6,1] => 9
[10,5,2] => 9
[10,5,1,1] => 9
[10,4,3] => 9
[10,4,2,1] => 9
[10,4,1,1,1] => 9
[10,3,3,1] => 9
[10,3,2,2] => 9
[10,3,2,1,1] => 9
[10,3,1,1,1,1] => 9
[10,2,2,2,1] => 9
[10,2,2,1,1,1] => 9
[10,2,1,1,1,1,1] => 9
[10,1,1,1,1,1,1,1] => 9
[9,8] => 7
[9,7,1] => 8
[9,6,2] => 8
[9,6,1,1] => 8
[9,5,3] => 8
[9,5,2,1] => 8
[9,5,1,1,1] => 8
[9,4,4] => 8
[9,4,3,1] => 8
[9,4,2,2] => 8
[9,4,2,1,1] => 8
[9,4,1,1,1,1] => 8
[9,3,3,2] => 8
[9,3,3,1,1] => 8
[9,3,2,2,1] => 8
[9,3,2,1,1,1] => 8
[9,3,1,1,1,1,1] => 8
[9,2,2,2,2] => 8
[9,2,2,2,1,1] => 8
[9,2,2,1,1,1,1] => 8
[9,2,1,1,1,1,1,1] => 8
[9,1,1,1,1,1,1,1,1] => 8
[8,8,1] => 7
[8,7,2] => 6
[8,7,1,1] => 6
[8,6,3] => 7
[8,6,2,1] => 7
[8,6,1,1,1] => 7
[8,5,4] => 7
[8,5,3,1] => 7
[8,5,2,2] => 7
[8,5,2,1,1] => 7
[8,5,1,1,1,1] => 7
[8,4,4,1] => 7
[8,4,3,2] => 7
[8,4,3,1,1] => 7
[8,4,2,2,1] => 7
[8,4,2,1,1,1] => 7
[8,4,1,1,1,1,1] => 7
[8,3,3,3] => 7
[8,3,3,2,1] => 7
[8,3,3,1,1,1] => 7
[8,3,2,2,2] => 7
[8,3,2,2,1,1] => 7
[8,3,2,1,1,1,1] => 7
[8,3,1,1,1,1,1,1] => 7
[8,2,2,2,2,1] => 7
[8,2,2,2,1,1,1] => 7
[8,2,2,1,1,1,1,1] => 7
[8,2,1,1,1,1,1,1,1] => 7
[8,1,1,1,1,1,1,1,1,1] => 7
[7,7,3] => 6
[7,7,2,1] => 6
[7,7,1,1,1] => 6
[7,6,4] => 5
[7,6,3,1] => 5
[7,6,2,2] => 5
[7,6,2,1,1] => 5
[7,6,1,1,1,1] => 5
[7,5,5] => 6
[7,5,4,1] => 6
[7,5,3,2] => 6
[7,5,3,1,1] => 6
[7,5,2,2,1] => 6
[7,5,2,1,1,1] => 6
[7,5,1,1,1,1,1] => 6
[7,4,4,2] => 6
[7,4,4,1,1] => 6
[7,4,3,3] => 6
[7,4,3,2,1] => 6
[7,4,3,1,1,1] => 6
[7,4,2,2,2] => 6
[7,4,2,2,1,1] => 6
[7,4,2,1,1,1,1] => 6
[7,4,1,1,1,1,1,1] => 6
[7,3,3,3,1] => 6
[7,3,3,2,2] => 6
[7,3,3,2,1,1] => 6
[7,3,3,1,1,1,1] => 6
[7,3,2,2,2,1] => 6
[7,3,2,2,1,1,1] => 6
[7,3,2,1,1,1,1,1] => 6
[7,3,1,1,1,1,1,1,1] => 6
[7,2,2,2,2,2] => 6
[7,2,2,2,2,1,1] => 6
[7,2,2,2,1,1,1,1] => 6
[7,2,2,1,1,1,1,1,1] => 6
[7,2,1,1,1,1,1,1,1,1] => 6
[7,1,1,1,1,1,1,1,1,1,1] => 6
[6,6,5] => 4
[6,6,4,1] => 5
[6,6,3,2] => 5
[6,6,3,1,1] => 5
[6,6,2,2,1] => 5
[6,6,2,1,1,1] => 5
[6,6,1,1,1,1,1] => 5
[6,5,5,1] => 4
[6,5,4,2] => 3
[6,5,4,1,1] => 3
[6,5,3,3] => 4
[6,5,3,2,1] => 4
[6,5,3,1,1,1] => 4
[6,5,2,2,2] => 4
[6,5,2,2,1,1] => 4
[6,5,2,1,1,1,1] => 4
[6,5,1,1,1,1,1,1] => 4
[6,4,4,3] => 5
[6,4,4,2,1] => 5
[6,4,4,1,1,1] => 5
[6,4,3,3,1] => 5
[6,4,3,2,2] => 5
[6,4,3,2,1,1] => 5
[6,4,3,1,1,1,1] => 5
[6,4,2,2,2,1] => 5
[6,4,2,2,1,1,1] => 5
[6,4,2,1,1,1,1,1] => 5
[6,4,1,1,1,1,1,1,1] => 5
[6,3,3,3,2] => 5
[6,3,3,3,1,1] => 5
[6,3,3,2,2,1] => 5
[6,3,3,2,1,1,1] => 5
[6,3,3,1,1,1,1,1] => 5
[6,3,2,2,2,2] => 5
[6,3,2,2,2,1,1] => 5
[6,3,2,2,1,1,1,1] => 5
[6,3,2,1,1,1,1,1,1] => 5
[6,3,1,1,1,1,1,1,1,1] => 5
[6,2,2,2,2,2,1] => 5
[6,2,2,2,2,1,1,1] => 5
[6,2,2,2,1,1,1,1,1] => 5
[6,2,2,1,1,1,1,1,1,1] => 5
[6,2,1,1,1,1,1,1,1,1,1] => 5
[6,1,1,1,1,1,1,1,1,1,1,1] => 5
[5,5,5,2] => 4
[5,5,5,1,1] => 4
[5,5,4,3] => 2
[5,5,4,2,1] => 3
[5,5,4,1,1,1] => 3
[5,5,3,3,1] => 4
[5,5,3,2,2] => 4
[5,5,3,2,1,1] => 4
[5,5,3,1,1,1,1] => 4
[5,5,2,2,2,1] => 4
[5,5,2,2,1,1,1] => 4
[5,5,2,1,1,1,1,1] => 4
[5,5,1,1,1,1,1,1,1] => 4
[5,4,4,4] => 3
[5,4,4,3,1] => 2
[5,4,4,2,2] => 3
[5,4,4,2,1,1] => 3
[5,4,4,1,1,1,1] => 3
[5,4,3,3,2] => 1
[5,4,3,3,1,1] => 2
[5,4,3,2,2,1] => 0
[5,4,3,2,1,1,1] => 0
[5,4,3,1,1,1,1,1] => 2
[5,4,2,2,2,2] => 3
[5,4,2,2,2,1,1] => 3
[5,4,2,2,1,1,1,1] => 3
[5,4,2,1,1,1,1,1,1] => 3
[5,4,1,1,1,1,1,1,1,1] => 3
[5,3,3,3,3] => 4
[5,3,3,3,2,1] => 4
[5,3,3,3,1,1,1] => 4
[5,3,3,2,2,2] => 4
[5,3,3,2,2,1,1] => 4
[5,3,3,2,1,1,1,1] => 4
[5,3,3,1,1,1,1,1,1] => 4
[5,3,2,2,2,2,1] => 4
[5,3,2,2,2,1,1,1] => 4
[5,3,2,2,1,1,1,1,1] => 4
[5,3,2,1,1,1,1,1,1,1] => 4
[5,3,1,1,1,1,1,1,1,1,1] => 4
[5,2,2,2,2,2,2] => 4
[5,2,2,2,2,2,1,1] => 4
[5,2,2,2,2,1,1,1,1] => 4
[5,2,2,2,1,1,1,1,1,1] => 4
[5,2,2,1,1,1,1,1,1,1,1] => 4
[5,2,1,1,1,1,1,1,1,1,1,1] => 4
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 4
[4,4,4,4,1] => 3
[4,4,4,3,2] => 1
[4,4,4,3,1,1] => 2
[4,4,4,2,2,1] => 3
[4,4,4,2,1,1,1] => 3
[4,4,4,1,1,1,1,1] => 3
[4,4,3,3,3] => 2
[4,4,3,3,2,1] => 0
[4,4,3,3,1,1,1] => 2
[4,4,3,2,2,2] => 1
[4,4,3,2,2,1,1] => 0
[4,4,3,2,1,1,1,1] => 0
[4,4,3,1,1,1,1,1,1] => 2
[4,4,2,2,2,2,1] => 3
[4,4,2,2,2,1,1,1] => 3
[4,4,2,2,1,1,1,1,1] => 3
[4,4,2,1,1,1,1,1,1,1] => 3
[4,4,1,1,1,1,1,1,1,1,1] => 3
[4,3,3,3,3,1] => 2
[4,3,3,3,2,2] => 1
[4,3,3,3,2,1,1] => 0
[4,3,3,3,1,1,1,1] => 2
[4,3,3,2,2,2,1] => 0
[4,3,3,2,2,1,1,1] => 0
[4,3,3,2,1,1,1,1,1] => 0
[4,3,3,1,1,1,1,1,1,1] => 2
[4,3,2,2,2,2,2] => 1
[4,3,2,2,2,2,1,1] => 0
[4,3,2,2,2,1,1,1,1] => 0
[4,3,2,2,1,1,1,1,1,1] => 0
[4,3,2,1,1,1,1,1,1,1,1] => 0
[4,3,1,1,1,1,1,1,1,1,1,1] => 2
[4,2,2,2,2,2,2,1] => 3
[4,2,2,2,2,2,1,1,1] => 3
[4,2,2,2,2,1,1,1,1,1] => 3
[4,2,2,2,1,1,1,1,1,1,1] => 3
[4,2,2,1,1,1,1,1,1,1,1,1] => 3
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 3
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 3
[3,3,3,3,3,2] => 1
[3,3,3,3,3,1,1] => 2
[3,3,3,3,2,2,1] => 0
[3,3,3,3,2,1,1,1] => 0
[3,3,3,3,1,1,1,1,1] => 2
[3,3,3,2,2,2,2] => 1
[3,3,3,2,2,2,1,1] => 0
[3,3,3,2,2,1,1,1,1] => 0
[3,3,3,2,1,1,1,1,1,1] => 0
[3,3,3,1,1,1,1,1,1,1,1] => 2
[3,3,2,2,2,2,2,1] => 0
[3,3,2,2,2,2,1,1,1] => 0
[3,3,2,2,2,1,1,1,1,1] => 0
[3,3,2,2,1,1,1,1,1,1,1] => 0
[3,3,2,1,1,1,1,1,1,1,1,1] => 0
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 2
[3,2,2,2,2,2,2,2] => 1
[3,2,2,2,2,2,2,1,1] => 0
[3,2,2,2,2,2,1,1,1,1] => 0
[3,2,2,2,2,1,1,1,1,1,1] => 0
[3,2,2,2,1,1,1,1,1,1,1,1] => 0
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 0
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 2,0,1 2,1,1,1 3,1,1,1,1 4,1,2,2,1,1 5,1,3,2,2,1,1 6,2,3,4,3,2,1,1 8,2,4,5,4,3,2,1,1 10,2,5,7,6,5,3,2,1,1 12,3,6,8,9,6,5,3,2,1,1 15,3,8,11,11,10,7,5,3,2,1,1 18,4,9,13,15,13,10,7,5,3,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 2 + q^{2}$
$F_{4} = 2 + q + q^{2} + q^{3}$
$F_{5} = 3 + q + q^{2} + q^{3} + q^{4}$
$F_{6} = 4 + q + 2\ q^{2} + 2\ q^{3} + q^{4} + q^{5}$
$F_{7} = 5 + q + 3\ q^{2} + 2\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{8} = 6 + 2\ q + 3\ q^{2} + 4\ q^{3} + 3\ q^{4} + 2\ q^{5} + q^{6} + q^{7}$
$F_{9} = 8 + 2\ q + 4\ q^{2} + 5\ q^{3} + 4\ q^{4} + 3\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$
$F_{10} = 10 + 2\ q + 5\ q^{2} + 7\ q^{3} + 6\ q^{4} + 5\ q^{5} + 3\ q^{6} + 2\ q^{7} + q^{8} + q^{9}$
$F_{11} = 12 + 3\ q + 6\ q^{2} + 8\ q^{3} + 9\ q^{4} + 6\ q^{5} + 5\ q^{6} + 3\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{12} = 15 + 3\ q + 8\ q^{2} + 11\ q^{3} + 11\ q^{4} + 10\ q^{5} + 7\ q^{6} + 5\ q^{7} + 3\ q^{8} + 2\ q^{9} + q^{10} + q^{11}$
$F_{13} = 18 + 4\ q + 9\ q^{2} + 13\ q^{3} + 15\ q^{4} + 13\ q^{5} + 10\ q^{6} + 7\ q^{7} + 5\ q^{8} + 3\ q^{9} + 2\ q^{10} + q^{11} + q^{12}$
$F_{14} = 22 + 5\ q + 10\ q^{2} + 17\ q^{3} + 19\ q^{4} + 18\ q^{5} + 14\ q^{6} + 11\ q^{7} + 7\ q^{8} + 5\ q^{9} + 3\ q^{10} + 2\ q^{11} + q^{12} + q^{13}$
$F_{15} = 27 + 5\ q + 13\ q^{2} + 20\ q^{3} + 24\ q^{4} + 23\ q^{5} + 20\ q^{6} + 14\ q^{7} + 11\ q^{8} + 7\ q^{9} + 5\ q^{10} + 3\ q^{11} + 2\ q^{12} + q^{13} + q^{14}$
$F_{16} = 32 + 6\ q + 15\ q^{2} + 25\ q^{3} + 30\ q^{4} + 31\ q^{5} + 26\ q^{6} + 21\ q^{7} + 15\ q^{8} + 11\ q^{9} + 7\ q^{10} + 5\ q^{11} + 3\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
Description
The largest nonnegative integer which is not a part and is smaller than the largest part of the partition.
References
[1] Chern, S. Partitions and the maximal excludant arXiv:1905.06304
Code
def statistic(p):
return next(i for i in range(p[0]-1,-1,-1) if i not in p)
Created
May 16, 2019 at 08:11 by Martin Rubey
Updated
Mar 05, 2020 at 14:14 by Martin Rubey
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!