- FindStat

edit this statistic or download as text // json

Identifier

St001252: Integer partitions ⟶ ℤ

Values

[] => 0

[1] => 0

[2] => 1

[1,1] => 0

[3] => 0

[2,1] => 1

[1,1,1] => 0

[4] => 2

[3,1] => 0

[2,2] => 2

[2,1,1] => 1

[1,1,1,1] => 0

[5] => 0

[4,1] => 2

[3,2] => 1

[3,1,1] => 0

[2,2,1] => 2

[2,1,1,1] => 1

[1,1,1,1,1] => 0

[6] => 3

[5,1] => 0

[4,2] => 3

[4,1,1] => 2

[3,3] => 0

[3,2,1] => 1

[3,1,1,1] => 0

[2,2,2] => 3

[2,2,1,1] => 2

[2,1,1,1,1] => 1

[1,1,1,1,1,1] => 0

[7] => 0

[6,1] => 3

[5,2] => 1

[5,1,1] => 0

[4,3] => 2

[4,2,1] => 3

[4,1,1,1] => 2

[3,3,1] => 0

[3,2,2] => 2

[3,2,1,1] => 1

[3,1,1,1,1] => 0

[2,2,2,1] => 3

[2,2,1,1,1] => 2

[2,1,1,1,1,1] => 1

[1,1,1,1,1,1,1] => 0

[8] => 4

[7,1] => 0

[6,2] => 4

[6,1,1] => 3

[5,3] => 0

[5,2,1] => 1

[5,1,1,1] => 0

[4,4] => 4

[4,3,1] => 2

[4,2,2] => 4

[4,2,1,1] => 3

[4,1,1,1,1] => 2

[3,3,2] => 1

[3,3,1,1] => 0

[3,2,2,1] => 2

[3,2,1,1,1] => 1

[3,1,1,1,1,1] => 0

[2,2,2,2] => 4

[2,2,2,1,1] => 3

[2,2,1,1,1,1] => 2

[2,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1] => 0

[9] => 0

[8,1] => 4

[7,2] => 1

[7,1,1] => 0

[6,3] => 3

[6,2,1] => 4

[6,1,1,1] => 3

[5,4] => 2

[5,3,1] => 0

[5,2,2] => 2

[5,2,1,1] => 1

[5,1,1,1,1] => 0

[4,4,1] => 4

[4,3,2] => 3

[4,3,1,1] => 2

[4,2,2,1] => 4

[4,2,1,1,1] => 3

[4,1,1,1,1,1] => 2

[3,3,3] => 0

[3,3,2,1] => 1

[3,3,1,1,1] => 0

[3,2,2,2] => 3

[3,2,2,1,1] => 2

[3,2,1,1,1,1] => 1

[3,1,1,1,1,1,1] => 0

[2,2,2,2,1] => 4

[2,2,2,1,1,1] => 3

[2,2,1,1,1,1,1] => 2

[2,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1,1] => 0

[10] => 5

[9,1] => 0

[8,2] => 5

[8,1,1] => 4

>>> Load all 789 entries. <<<

[7,3] => 0

[7,2,1] => 1

[7,1,1,1] => 0

[6,4] => 5

[6,3,1] => 3

[6,2,2] => 5

[6,2,1,1] => 4

[6,1,1,1,1] => 3

[5,5] => 0

[5,4,1] => 2

[5,3,2] => 1

[5,3,1,1] => 0

[5,2,2,1] => 2

[5,2,1,1,1] => 1

[5,1,1,1,1,1] => 0

[4,4,2] => 5

[4,4,1,1] => 4

[4,3,3] => 2

[4,3,2,1] => 3

[4,3,1,1,1] => 2

[4,2,2,2] => 5

[4,2,2,1,1] => 4

[4,2,1,1,1,1] => 3

[4,1,1,1,1,1,1] => 2

[3,3,3,1] => 0

[3,3,2,2] => 2

[3,3,2,1,1] => 1

[3,3,1,1,1,1] => 0

[3,2,2,2,1] => 3

[3,2,2,1,1,1] => 2

[3,2,1,1,1,1,1] => 1

[3,1,1,1,1,1,1,1] => 0

[2,2,2,2,2] => 5

[2,2,2,2,1,1] => 4

[2,2,2,1,1,1,1] => 3

[2,2,1,1,1,1,1,1] => 2

[2,1,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1,1,1] => 0

[11] => 0

[10,1] => 5

[9,2] => 1

[9,1,1] => 0

[8,3] => 4

[8,2,1] => 5

[8,1,1,1] => 4

[7,4] => 2

[7,2,2] => 2

[7,2,1,1] => 1

[7,1,1,1,1] => 0

[6,5] => 3

[6,4,1] => 5

[6,3,2] => 4

[6,3,1,1] => 3

[6,2,2,1] => 5

[6,2,1,1,1] => 4

[6,1,1,1,1,1] => 3

[5,5,1] => 0

[5,4,2] => 3

[5,4,1,1] => 2

[5,3,3] => 0

[5,3,2,1] => 1

[5,3,1,1,1] => 0

[5,2,2,2] => 3

[5,2,2,1,1] => 2

[5,2,1,1,1,1] => 1

[5,1,1,1,1,1,1] => 0

[4,4,3] => 4

[4,4,2,1] => 5

[4,4,1,1,1] => 4

[4,3,3,1] => 2

[4,3,2,2] => 4

[4,3,2,1,1] => 3

[4,3,1,1,1,1] => 2

[4,2,2,2,1] => 5

[4,2,2,1,1,1] => 4

[4,1,1,1,1,1,1,1] => 2

[3,3,3,2] => 1

[3,3,3,1,1] => 0

[3,3,2,2,1] => 2

[3,3,2,1,1,1] => 1

[3,3,1,1,1,1,1] => 0

[3,2,2,2,2] => 4

[3,2,2,2,1,1] => 3

[3,2,2,1,1,1,1] => 2

[3,2,1,1,1,1,1,1] => 1

[3,1,1,1,1,1,1,1,1] => 0

[2,2,2,2,2,1] => 5

[2,2,2,2,1,1,1] => 4

[2,2,2,1,1,1,1,1] => 3

[2,2,1,1,1,1,1,1,1] => 2

[2,1,1,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1,1,1,1] => 0

[12] => 6

[11,1] => 0

[10,2] => 6

[10,1,1] => 5

[9,3] => 0

[9,2,1] => 1

[9,1,1,1] => 0

[8,4] => 6

[8,3,1] => 4

[8,2,2] => 6

[8,2,1,1] => 5

[8,1,1,1,1] => 4

[7,5] => 0

[7,4,1] => 2

[7,3,2] => 1

[7,3,1,1] => 0

[7,2,2,1] => 2

[7,1,1,1,1,1] => 0

[6,6] => 6

[6,5,1] => 3

[6,4,2] => 6

[6,4,1,1] => 5

[6,3,3] => 3

[6,3,1,1,1] => 3

[6,2,2,2] => 6

[6,2,2,1,1] => 5

[6,2,1,1,1,1] => 4

[6,1,1,1,1,1,1] => 3

[5,5,2] => 1

[5,5,1,1] => 0

[5,4,3] => 2

[5,4,2,1] => 3

[5,4,1,1,1] => 2

[5,3,3,1] => 0

[5,3,2,2] => 2

[5,3,2,1,1] => 1

[5,3,1,1,1,1] => 0

[5,2,2,2,1] => 3

[5,2,2,1,1,1] => 2

[5,2,1,1,1,1,1] => 1

[5,1,1,1,1,1,1,1] => 0

[4,4,4] => 6

[4,4,3,1] => 4

[4,4,2,2] => 6

[4,4,2,1,1] => 5

[4,3,3,2] => 3

[4,3,3,1,1] => 2

[4,3,2,2,1] => 4

[4,3,1,1,1,1,1] => 2

[4,2,2,2,2] => 6

[4,2,2,1,1,1,1] => 4

[4,2,1,1,1,1,1,1] => 3

[4,1,1,1,1,1,1,1,1] => 2

[3,3,3,3] => 0

[3,3,3,2,1] => 1

[3,3,3,1,1,1] => 0

[3,3,2,2,2] => 3

[3,3,2,2,1,1] => 2

[3,3,1,1,1,1,1,1] => 0

[3,2,2,2,2,1] => 4

[3,2,2,1,1,1,1,1] => 2

[3,2,1,1,1,1,1,1,1] => 1

[3,1,1,1,1,1,1,1,1,1] => 0

[2,2,2,2,2,2] => 6

[2,2,2,2,2,1,1] => 5

[2,2,2,2,1,1,1,1] => 4

[2,2,2,1,1,1,1,1,1] => 3

[2,2,1,1,1,1,1,1,1,1] => 2

[2,1,1,1,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1,1,1,1,1] => 0

[13] => 0

[12,1] => 6

[10,3] => 5

[9,4] => 2

[9,2,2] => 2

[9,2,1,1] => 1

[8,5] => 4

[8,4,1] => 6

[8,3,2] => 5

[8,3,1,1] => 4

[7,6] => 3

[7,5,1] => 0

[7,4,2] => 3

[7,4,1,1] => 2

[7,3,3] => 0

[7,3,2,1] => 1

[7,2,2,2] => 3

[7,2,1,1,1,1] => 1

[7,1,1,1,1,1,1] => 0

[6,6,1] => 6

[6,5,2] => 4

[6,5,1,1] => 3

[6,4,3] => 5

[6,4,2,1] => 6

[6,3,3,1] => 3

[6,3,2,2] => 5

[6,3,1,1,1,1] => 3

[6,2,2,2,1] => 6

[6,2,2,1,1,1] => 5

[6,1,1,1,1,1,1,1] => 3

[5,5,3] => 0

[5,5,2,1] => 1

[5,4,4] => 4

[5,4,3,1] => 2

[5,4,2,2] => 4

[5,4,2,1,1] => 3

[5,4,1,1,1,1] => 2

[5,3,3,2] => 1

[5,3,3,1,1] => 0

[5,3,2,2,1] => 2

[5,3,2,1,1,1] => 1

[5,3,1,1,1,1,1] => 0

[5,2,2,2,1,1] => 3

[5,2,2,1,1,1,1] => 2

[5,2,1,1,1,1,1,1] => 1

[4,4,4,1] => 6

[4,4,3,2] => 5

[4,4,3,1,1] => 4

[4,4,2,2,1] => 6

[4,3,3,3] => 2

[4,3,3,2,1] => 3

[4,2,2,2,2,1] => 6

[3,3,3,3,1] => 0

[3,3,3,2,2] => 2

[3,3,3,2,1,1] => 1

[3,3,2,2,2,1] => 3

[3,3,2,2,1,1,1] => 2

[3,3,2,1,1,1,1,1] => 1

[3,3,1,1,1,1,1,1,1] => 0

[3,2,2,2,2,2] => 5

[3,2,2,2,2,1,1] => 4

[3,2,2,1,1,1,1,1,1] => 2

[3,2,1,1,1,1,1,1,1,1] => 1

[3,1,1,1,1,1,1,1,1,1,1] => 0

[2,2,2,2,2,2,1] => 6

[2,2,2,2,1,1,1,1,1] => 4

[2,2,2,1,1,1,1,1,1,1] => 3

[2,2,1,1,1,1,1,1,1,1,1] => 2

[2,1,1,1,1,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[14] => 7

[13,1] => 0

[12,2] => 7

[12,1,1] => 6

[11,2,1] => 1

[11,1,1,1] => 0

[10,2,2] => 7

[9,5] => 0

[9,4,1] => 2

[9,2,2,1] => 2

[8,6] => 7

[8,5,1] => 4

[8,4,2] => 7

[8,3,3] => 4

[8,3,1,1,1] => 4

[8,1,1,1,1,1,1] => 4

[7,7] => 0

[7,6,1] => 3

[7,5,2] => 1

[7,4,3] => 2

[7,2,2,2,1] => 3

[6,6,2] => 7

[6,6,1,1] => 6

[6,5,3] => 3

[6,5,1,1,1] => 3

[6,4,4] => 7

[6,4,2,2] => 7

[6,2,2,2,2] => 7

[6,1,1,1,1,1,1,1,1] => 3

[5,5,4] => 2

[5,5,1,1,1,1] => 0

[5,4,4,1] => 4

[5,4,3,2] => 3

[5,4,3,1,1] => 2

[5,4,2,2,1] => 4

[5,4,2,1,1,1] => 3

[5,4,1,1,1,1,1] => 2

[5,3,3,3] => 0

[5,3,3,2,1] => 1

[5,3,2,2,2] => 3

[5,3,2,2,1,1] => 2

[5,3,2,1,1,1,1] => 1

[5,3,1,1,1,1,1,1] => 0

[5,2,2,2,2,1] => 4

[5,2,2,1,1,1,1,1] => 2

[4,4,4,2] => 7

[4,4,4,1,1] => 6

[4,4,3,3] => 4

[4,4,3,2,1] => 5

[4,3,2,2,2,1] => 5

[3,3,3,3,2] => 1

[3,3,3,3,1,1] => 0

[3,3,3,2,2,1] => 2

[3,3,2,2,2,2] => 4

[3,3,1,1,1,1,1,1,1,1] => 0

[3,2,2,2,2,1,1,1] => 4

[2,2,2,2,2,2,2] => 7

[2,2,2,2,1,1,1,1,1,1] => 4

[2,2,2,1,1,1,1,1,1,1,1] => 3

[2,2,1,1,1,1,1,1,1,1,1,1] => 2

[2,1,1,1,1,1,1,1,1,1,1,1,1] => 1

[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[15] => 0

[14,1] => 7

[12,3] => 6

[11,2,2] => 2

[9,6] => 3

[9,5,1] => 0

[9,3,2,1] => 1

[8,7] => 4

[8,5,2] => 5

[7,5,3] => 0

[6,6,3] => 6

[6,5,4] => 5

[6,5,1,1,1,1] => 3

[6,4,3,1,1] => 5

[6,3,3,3] => 3

[6,3,1,1,1,1,1,1] => 3

[6,2,2,2,2,1] => 7

[5,5,5] => 0

[5,5,2,2,1] => 2

[5,4,3,3] => 2

[5,4,3,2,1] => 3

[5,4,3,1,1,1] => 2

[5,3,2,2,2,1] => 3

[5,3,2,2,1,1,1] => 2

[5,3,1,1,1,1,1,1,1] => 0

[4,4,4,3] => 6

[4,4,4,1,1,1] => 6

[4,3,3,3,2] => 3

[3,3,3,3,3] => 0

[3,3,3,3,2,1] => 1

[3,3,3,2,2,2] => 3

[2,2,2,2,2,2,2,1] => 7

[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[16] => 8

[15,1] => 0

[12,4] => 8

[12,1,1,1,1] => 6

[10,6] => 8

[9,1,1,1,1,1,1,1] => 0

[8,8] => 8

[8,6,2] => 8

[8,5,3] => 4

[7,6,3] => 3

[7,5,3,1] => 0

[7,5,1,1,1,1] => 0

[7,3,3,2,1] => 1

[6,6,4] => 8

[6,6,2,2] => 8

[6,5,5] => 3

[6,4,3,3] => 5

[5,5,3,3] => 0

[5,5,2,2,2] => 3

[5,4,4,3] => 4

[5,4,3,2,1,1] => 3

[5,4,2,2,2,1] => 5

[4,4,4,4] => 8

[4,4,4,2,2] => 8

[4,4,3,3,2] => 5

[4,4,2,2,2,2] => 8

[4,3,3,3,3] => 2

[4,3,3,3,2,1] => 3

[3,3,3,3,3,1] => 0

[3,3,3,3,2,2] => 2

[3,3,3,3,1,1,1,1] => 0

[3,3,2,2,2,2,2] => 5

[2,2,2,2,2,2,2,2] => 8

[2,2,2,2,2,2,1,1,1,1] => 6

[2,2,2,2,1,1,1,1,1,1,1,1] => 4

[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[17] => 0

[16,1] => 8

[9,8] => 4

[8,8,1] => 8

[8,6,3] => 7

[7,6,1,1,1,1] => 3

[7,5,3,2] => 1

[6,5,3,3] => 3

[6,5,2,2,2] => 6

[6,4,4,3] => 7

[6,4,4,1,1,1] => 7

[6,3,3,3,2] => 4

[6,3,3,3,1,1] => 3

[5,5,4,3] => 2

[5,5,4,1,1,1] => 2

[5,5,2,2,2,1] => 3

[5,4,4,4] => 6

[5,4,3,2,2,1] => 4

[5,3,3,3,2,1] => 1

[4,4,4,3,2] => 7

[4,4,4,3,1,1] => 6

[4,4,4,2,2,1] => 8

[4,4,3,3,3] => 4

[3,3,3,3,3,2] => 1

[3,2,2,2,2,2,2,2] => 7

[3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[4,4,4,3,2,1] => 7

[5,4,3,3,2,1] => 3

[6,3,3,3,2,1] => 4

[6,5,2,2,2,1] => 6

[5,5,3,3,1,1] => 0

[6,5,4,1,1,1] => 5

[5,5,3,3,2] => 1

[5,5,4,2,2] => 4

[6,4,4,2,2] => 9

[6,5,4,3] => 5

[3,3,3,3,3,2,1] => 1

[4,4,4,3,3] => 6

[4,4,4,4,2] => 9

[5,5,4,4] => 4

[6,4,4,4] => 9

[7,6,5] => 3

[2,2,2,2,2,2,2,2,2] => 9

[3,3,3,3,3,3] => 0

[18] => 9

[6,2,2,2,2,2,2] => 9

[6,6,6] => 9

[4,2,2,2,2,2,2,2] => 9

[10,4,4] => 9

[9,6,3] => 3

[8,6,4] => 9

[10,8] => 9

[3,3,3,3,1,1,1,1,1,1] => 0

[9,9] => 0

[7,7,1,1,1,1] => 0

[9,1,1,1,1,1,1,1,1,1] => 0

[7,7,4] => 2

[5,4,4,3,2,1] => 5

[5,5,3,3,2,1] => 1

[5,5,4,2,2,1] => 4

[6,4,4,2,2,1] => 9

[5,5,4,3,1,1] => 2

[6,4,4,3,1,1] => 7

[6,5,3,3,1,1] => 3

[5,5,4,3,2] => 3

[6,4,4,3,2] => 8

[6,5,3,3,2] => 4

[6,5,4,2,2] => 7

[6,5,4,3,1] => 5

[6,5,4,1,1,1,1] => 5

[4,4,4,4,3] => 8

[4,3,3,3,3,3] => 2

[19] => 0

[7,2,2,2,2,2,2] => 6

[7,6,6] => 6

[5,2,2,2,2,2,2,2] => 7

[13,6] => 3

[11,4,4] => 4

[9,6,4] => 5

[8,5,4,2] => 7

[8,5,5,1] => 4

[5,5,4,3,2,1] => 3

[6,4,4,3,2,1] => 8

[6,5,3,3,2,1] => 4

[6,5,4,2,2,1] => 7

[6,5,4,3,1,1] => 5

[6,5,4,3,2] => 6

[6,5,2,2,2,2,1] => 7

[6,5,4,2,1,1,1] => 6

[6,6,2,2,2,2] => 10

[7,5,4,3,1] => 2

[2,2,2,2,2,2,2,2,2,2] => 10

[3,3,3,3,3,3,2] => 1

[4,4,3,3,3,3] => 4

[4,4,4,4,4] => 10

[5,5,5,5] => 0

[20] => 10

[10,10] => 10

[8,2,2,2,2,2,2] => 10

[8,6,4,2] => 10

[8,6,6] => 10

[10,6,4] => 10

[9,8,3] => 4

[6,6,6,2] => 10

[10,7,3] => 5

[9,7,4] => 2

[9,5,5,1] => 0

[12,5,1,1,1] => 6

[11,1,1,1,1,1,1,1,1,1] => 0

[6,5,4,3,2,1] => 6

[6,3,3,3,3,2,1] => 4

[6,5,3,2,2,2,1] => 6

[6,5,4,3,1,1,1] => 5

[7,6,2,2,2,2] => 7

[6,6,5,4] => 8

[3,3,3,3,3,3,3] => 0

[4,4,4,3,3,3] => 6

[21] => 0

[11,7,3] => 0

[5,4,2,2,2,2,2,2] => 8

[11,10] => 5

[13,4,4] => 4

[7,6,6,2] => 7

[4,4,4,4,3,2,1] => 9

[6,4,3,3,3,2,1] => 6

[6,5,4,2,2,2,1] => 8

[6,5,4,3,2,1,1] => 6

[4,4,4,4,3,3] => 8

[8,6,2,2,2,2] => 11

[22] => 11

[9,6,4,3] => 5

[8,7,7] => 4

[5,4,4,4,3,2,1] => 7

[6,5,3,3,3,2,1] => 4

[6,5,4,3,2,2,1] => 7

[15,2,2,2,2] => 4

[9,6,5,3] => 3

[8,6,5,3,1] => 7

[6,4,4,4,3,2,1] => 10

[6,5,4,3,3,2,1] => 6

[3,3,3,3,3,3,3,3] => 0

[4,4,4,4,4,4] => 12

[6,6,6,6] => 12

[24] => 12

[11,7,5,1] => 0

[9,7,5,3] => 0

[8,8,8] => 12

[3,3,3,3,3,3,3,2,1] => 1

[17,7] => 0

[12,9,3] => 6

[9,8,1,1,1,1,1,1,1] => 4

[13,1,1,1,1,1,1,1,1,1,1,1] => 0

[5,5,5,4,3,2,1] => 3

[6,5,4,4,3,2,1] => 8

[7,6,6,6] => 9

[5,4,4,4,2,2,2,2] => 10

[13,12] => 6

[15,5,5] => 0

[9,7,5,3,1] => 0

[10,7,5,3] => 5

[3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 0

[5,5,5,5,5] => 0

[12,10,3] => 11

[11,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[6,5,5,4,3,2,1] => 6

[6,6,4,3,3,2,2] => 10

[8,6,6,6] => 13

[9,7,5,4,1] => 2

[16,8,2] => 13

[6,6,5,4,3,2,1] => 9

[7,6,5,4,3,2] => 6

[3,3,3,3,3,3,3,3,3] => 0

[15,6,6] => 6

[7,6,5,4,3,2,1] => 6

[6,6,6,4,3,3] => 11

[4,3,3,3,3,3,3,3,3] => 2

[7,6,5,4,3,1,1,1] => 5

[10,7,6,4,1] => 10

[9,7,6,4,2] => 6

[10,8,5,4,1] => 11

[15,14] => 7

[7,6,5,4,3,2,1,1] => 6

[7,6,5,4,2,2,2,1] => 8

[10,8,6,4,1] => 14

[6,6,6,6,6] => 15

[30] => 15

[15,15] => 0

[5,5,5,5,5,5] => 0

[6,6,6,6,3,3] => 12

[10,10,10] => 15

[9,7,5,5,3,1] => 0

[7,6,5,4,3,2,2,1] => 7

[7,6,5,3,3,3,2,1] => 4

[11,8,6,4,1] => 9

[10,8,6,4,2] => 15

[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 15

[3,3,3,3,3,3,3,3,3,2,1] => 1

[7,6,6,6,6] => 12

[7,6,5,4,3,3,2,1] => 6

[7,6,4,4,4,3,2,1] => 10

[11,8,6,5,1] => 7

[10,10,9,2] => 11

[14,9,8] => 11

[4,4,4,4,4,4,4,4] => 16

[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 16

[7,6,5,4,4,3,2,1] => 8

[7,5,5,5,4,3,2,1] => 3

[16,16] => 16

[10,10,10,2] => 16

[16,8,4,2,2] => 16

[9,4,4,4,4,4,2,1] => 11

[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 15

[5,4,4,4,4,4,4,4] => 14

[7,6,5,5,4,3,2,1] => 6

[6,6,6,5,4,3,2,1] => 12

[22,7,4] => 13

[12,12,4,3,2] => 15

[4,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 17

[7,6,6,5,4,3,2,1] => 9

[12,9,7,5,1] => 6

[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 14

[7,7,6,5,4,3,2,1] => 6

[13,9,7,5,1] => 0

[18,18] => 18

[24,12] => 18

[11,9,7,5,3,1] => 0

[11,8,7,5,4,1] => 6

[8,7,6,5,4,3,2,1] => 10

[8,7,7,7,7] => 4

[7,6,2,2,2,2,2,2,2,2,2,2,2,2] => 15

[7,6,6,6,6,6] => 15

[8,7,6,5,4,3,2,1,1] => 10

[8,7,6,5,4,3,2,2,1] => 11

[8,7,6,5,4,3,3,2,1] => 10

[10,10,10,10] => 20

[12,12,12,4] => 20

[8,7,6,5,4,4,3,2,1] => 12

[11,9,7,5,5,3] => 0

[4,4,4,4,4,4,4,4,4,4] => 20

[14,14,8,4] => 20

[21,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0

[7,6,6,6,2,2,2,2,2,2,2,2] => 17

[8,7,6,5,5,4,3,2,1] => 10

[9,9,9,9,3,3] => 0

[8,7,6,6,5,4,3,2,1] => 13

[10,10,10,5,5,2] => 16

[16,10,8,8] => 21

[26,9,7] => 13

[8,7,7,6,5,4,3,2,1] => 10

[8,8,7,6,5,4,3,2,1] => 14

[18,18,9] => 18

[9,8,7,6,5,4,3,2,1] => 10

[11,9,7,7,5,3,3] => 0

[48] => 24

[7,6,6,6,6,6,6,6] => 21

[22,9,8,5,5] => 15

[6,6,6,6,6,6,6,3,3,2] => 22

[27,14,9] => 7

[17,14,13,8] => 11

[5,5,5,5,5,5,5,5,5,5,5] => 0

[27,20,8] => 14

[26,13,7,7,2] => 14

[31,12,10,4] => 13

[6,6,6,6,6,6,6,6,6,6] => 30

[5,5,5,5,5,5,5,5,5,5,5,5] => 0

[12,12,12,12,12] => 30

[17,16,2,2,2,2,2,2,2,2,2,2,2,2,2,1] => 21

[12,12,12,12,11,4] => 26

[12,12,12,12,12,4] => 32

[3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 31

[11,11,11,11,11,10] => 5

[11,11,11,11,11,11] => 0

[16,14,9,9,9,9] => 15

[8,8,8,8,8,8,8,8,4,2] => 35

[24,24,24] => 36

[16,16,16,16,8,4,2] => 39

[12,12,12,12,12,12,4,4] => 40

[22,20,20,12,8] => 41

[20,20,8,4,4,4,4,4,4,4,4,4] => 42

[33,32,9,9,5] => 16

[18,18,18,18,18] => 45

[18,18,18,18,9,9] => 36

[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 42

[56,17,11,10,5] => 33

[33,26,23,12,9] => 19

[22,22,22,10,10,9,4,4] => 47

[22,22,22,10,10,10,4,4] => 52

[12,12,12,12,12,12,12,12,4,3,2] => 51

[24,24,24,24,14] => 55

[76,22,9,6] => 52

[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 0

[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => 0

[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 60

[12,12,12,12,12,12,12,12,12,12] => 60

[24,24,24,24,24] => 60

[23,22,21,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,1] => 12

[12,12,12,12,12,12,12,12,12,6,6,6,4,2] => 66

[54,48,18,10,8] => 69

[24,24,24,24,24,24] => 72

[37,33,20,20,13,10,10,10,7] => 35

[42,34,30,22,22,14,2] => 83

[54,52,34,18,11,7] => 79

[65,27,27,25,13,9,6,6] => 6

[18,18,18,18,18,18,18,18,18,18] => 90

[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 90

[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2] => 91

[58,38,38,38,30] => 101

[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 120

[10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,2] => 126

[74,58,34,34,22,22,13,11,2] => 123

[61,48,48,48,45,22,12,2] => 90

[15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 0

[98,62,36,26,14,14,14,14,14,14,12,2] => 160

[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,13,2] => 169

[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,2] => 176

[74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3] => 172

[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 180

[64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6] => 104

[70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3] => 154

[14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,7,7,7,7,7,2] => 197

[170,92,36,28,27,24,20,14,13,10,8,8] => 205

[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,6,6,6,6,4,4,4,3,3] => 228

[145,83,62,44,44,42,19,16,16,10,8] => 121

[98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8] => 212

[6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6] => 360

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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 2,1 2,1,2 3,2,2 4,2,2,3 5,3,4,3 6,4,4,3,5 8,5,6,6,5 10,6,8,6,5,7

$F_{1} = 1$

$F_{2} = 1 + q$

$F_{3} = 2 + q$

$F_{4} = 2 + q + 2\ q^{2}$

$F_{5} = 3 + 2\ q + 2\ q^{2}$

$F_{6} = 4 + 2\ q + 2\ q^{2} + 3\ q^{3}$

$F_{7} = 5 + 3\ q + 4\ q^{2} + 3\ q^{3}$

$F_{8} = 6 + 4\ q + 4\ q^{2} + 3\ q^{3} + 5\ q^{4}$

$F_{9} = 8 + 5\ q + 6\ q^{2} + 6\ q^{3} + 5\ q^{4}$

$F_{10} = 10 + 6\ q + 8\ q^{2} + 6\ q^{3} + 5\ q^{4} + 7\ q^{5}$

Description

Half the sum of the even parts of a partition.

Code

def statistic(L):
    return sum(i for i in L if is_even(i))//2

Created

Sep 10, 2018 at 11:41 by Martin Rubey

Updated

Mar 25, 2024 at 23:43 by Martin Rubey

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