- FindStat

edit this statistic or download as text // json

Identifier

St001814: Integer partitions ⟶ ℤ

Values

[] => 1

[1] => 2

[2] => 3

[1,1] => 2

[3] => 4

[2,1] => 4

[1,1,1] => 2

[4] => 5

[3,1] => 6

[2,2] => 3

[2,1,1] => 4

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

[5] => 6

[4,1] => 8

[3,2] => 6

[3,1,1] => 6

[2,2,1] => 4

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

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

[6] => 7

[5,1] => 10

[4,2] => 9

[4,1,1] => 8

[3,3] => 4

[3,2,1] => 8

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

[2,2,2] => 3

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

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

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

[7] => 8

[6,1] => 12

[5,2] => 12

[5,1,1] => 10

[4,3] => 8

[4,2,1] => 12

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

[3,3,1] => 6

[3,2,2] => 6

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

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

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

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

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

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

[8] => 9

[7,1] => 14

[6,2] => 15

[6,1,1] => 12

[5,3] => 12

[5,2,1] => 16

[5,1,1,1] => 10

[4,4] => 5

[4,3,1] => 12

[4,2,2] => 9

[4,2,1,1] => 12

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

[3,3,2] => 6

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

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

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

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

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

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

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

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

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

[9] => 10

[8,1] => 16

[7,2] => 18

[7,1,1] => 14

[6,3] => 16

[6,2,1] => 20

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

[5,4] => 10

[5,3,1] => 18

[5,2,2] => 12

[5,2,1,1] => 16

[5,1,1,1,1] => 10

[4,4,1] => 8

[4,3,2] => 12

[4,3,1,1] => 12

[4,2,2,1] => 12

[4,2,1,1,1] => 12

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

[3,3,3] => 4

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

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

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

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

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

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

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

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

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

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

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

[10] => 11

[9,1] => 18

[8,2] => 21

[8,1,1] => 16

>>> Load all 709 entries. <<<

[7,3] => 20

[7,2,1] => 24

[7,1,1,1] => 14

[6,4] => 15

[6,3,1] => 24

[6,2,2] => 15

[6,2,1,1] => 20

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

[5,5] => 6

[5,4,1] => 16

[5,3,2] => 18

[5,3,1,1] => 18

[5,2,2,1] => 16

[5,2,1,1,1] => 16

[5,1,1,1,1,1] => 10

[4,4,2] => 9

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

[4,3,3] => 8

[4,3,2,1] => 16

[4,3,1,1,1] => 12

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

[4,2,2,1,1] => 12

[4,2,1,1,1,1] => 12

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[11] => 12

[10,1] => 20

[9,1,1] => 18

[8,3] => 24

[8,2,1] => 28

[8,1,1,1] => 16

[7,4] => 20

[7,2,2] => 18

[7,1,1,1,1] => 14

[6,5] => 12

[6,4,1] => 24

[6,3,2] => 24

[6,3,1,1] => 24

[6,2,2,1] => 20

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

[5,5,1] => 10

[5,4,2] => 18

[5,4,1,1] => 16

[5,3,3] => 12

[5,3,2,1] => 24

[5,3,1,1,1] => 18

[5,2,2,2] => 12

[5,2,2,1,1] => 16

[5,2,1,1,1,1] => 16

[5,1,1,1,1,1,1] => 10

[4,4,3] => 8

[4,4,2,1] => 12

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

[4,3,3,1] => 12

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

[4,3,2,1,1] => 16

[4,3,1,1,1,1] => 12

[4,2,2,2,1] => 12

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[12] => 13

[11,1] => 22

[10,2] => 27

[10,1,1] => 20

[9,3] => 28

[8,4] => 25

[8,3,1] => 36

[8,2,2] => 21

[8,2,1,1] => 28

[8,1,1,1,1] => 16

[7,5] => 18

[7,4,1] => 32

[6,6] => 7

[6,5,1] => 20

[6,4,2] => 27

[6,4,1,1] => 24

[6,3,3] => 16

[6,3,1,1,1] => 24

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

[6,2,2,1,1] => 20

[6,2,1,1,1,1] => 20

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

[5,5,2] => 12

[5,5,1,1] => 10

[5,4,3] => 16

[5,4,2,1] => 24

[5,4,1,1,1] => 16

[5,3,3,1] => 18

[5,3,2,2] => 18

[5,3,2,1,1] => 24

[5,3,1,1,1,1] => 18

[5,2,2,2,1] => 16

[5,2,2,1,1,1] => 16

[5,2,1,1,1,1,1] => 16

[5,1,1,1,1,1,1,1] => 10

[4,4,4] => 5

[4,4,3,1] => 12

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

[4,4,2,1,1] => 12

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

[4,3,3,1,1] => 12

[4,3,2,2,1] => 16

[4,3,1,1,1,1,1] => 12

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

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

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

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

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

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

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

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

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

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

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

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

[13] => 14

[12,1] => 24

[10,3] => 32

[9,2,2] => 24

[8,5] => 24

[8,4,1] => 40

[8,3,2] => 36

[8,3,1,1] => 36

[7,6] => 14

[7,5,1] => 30

[7,4,2] => 36

[7,3,3] => 20

[6,6,1] => 12

[6,5,2] => 24

[6,5,1,1] => 20

[6,4,3] => 24

[6,4,2,1] => 36

[6,3,2,2] => 24

[6,3,1,1,1,1] => 24

[6,2,2,1,1,1] => 20

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

[5,5,3] => 12

[5,4,4] => 10

[5,4,3,1] => 24

[5,4,2,2] => 18

[5,4,2,1,1] => 24

[5,4,1,1,1,1] => 16

[5,3,3,2] => 18

[5,3,3,1,1] => 18

[5,3,2,2,1] => 24

[5,3,2,1,1,1] => 24

[5,3,1,1,1,1,1] => 18

[5,2,2,2,1,1] => 16

[5,2,2,1,1,1,1] => 16

[5,2,1,1,1,1,1,1] => 16

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

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

[4,4,3,1,1] => 12

[4,4,2,2,1] => 12

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

[4,3,3,2,1] => 16

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

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

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

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

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

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

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

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

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

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

[14] => 15

[13,1] => 26

[12,2] => 33

[12,1,1] => 24

[9,5] => 30

[8,6] => 21

[8,5,1] => 40

[8,4,2] => 45

[8,3,1,1,1] => 36

[7,7] => 8

[7,5,2] => 36

[7,4,3] => 32

[6,6,2] => 15

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

[6,5,3] => 24

[6,5,1,1,1] => 20

[6,4,4] => 15

[6,4,2,2] => 27

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

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

[5,5,4] => 10

[5,5,1,1,1,1] => 10

[5,4,3,2] => 24

[5,4,3,1,1] => 24

[5,4,2,2,1] => 24

[5,4,2,1,1,1] => 24

[5,4,1,1,1,1,1] => 16

[5,3,3,3] => 12

[5,3,3,2,1] => 24

[5,3,2,2,2] => 18

[5,3,2,2,1,1] => 24

[5,3,2,1,1,1,1] => 24

[5,3,1,1,1,1,1,1] => 18

[5,2,2,2,2,1] => 16

[5,2,2,1,1,1,1,1] => 16

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

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

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

[4,4,3,2,1] => 16

[4,3,2,2,2,1] => 16

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

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

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

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

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

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

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

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

[15] => 16

[14,1] => 28

[12,3] => 40

[11,2,2] => 30

[9,6] => 28

[9,5,1] => 50

[8,7] => 16

[8,5,2] => 48

[7,5,3] => 36

[6,6,3] => 16

[6,5,4] => 20

[6,5,1,1,1,1] => 20

[6,4,3,1,1] => 36

[6,3,3,3] => 16

[6,3,1,1,1,1,1,1] => 24

[6,2,2,2,2,1] => 20

[5,5,5] => 6

[5,4,3,3] => 16

[5,4,3,2,1] => 32

[5,4,3,1,1,1] => 24

[5,3,2,2,2,1] => 24

[5,3,2,2,1,1,1] => 24

[5,3,1,1,1,1,1,1,1] => 18

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

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

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

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

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

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

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

[16] => 17

[15,1] => 30

[12,4] => 45

[12,1,1,1,1] => 24

[10,6] => 35

[8,8] => 9

[8,6,2] => 45

[8,5,3] => 48

[7,6,3] => 32

[7,5,3,1] => 54

[6,6,4] => 15

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

[6,5,5] => 12

[6,4,3,3] => 24

[5,5,3,3] => 12

[5,5,2,2,2] => 12

[5,4,4,3] => 16

[5,4,3,2,1,1] => 32

[5,4,2,2,2,1] => 24

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

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

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

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

[4,3,3,3,2,1] => 16

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

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

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

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

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

[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] => 2

[17] => 18

[9,8] => 18

[8,8,1] => 16

[8,6,3] => 48

[7,5,3,2] => 54

[6,5,3,3] => 24

[6,5,2,2,2] => 24

[6,4,4,3] => 24

[6,4,4,1,1,1] => 24

[6,3,3,3,2] => 24

[6,3,3,3,1,1] => 24

[5,5,4,3] => 16

[5,5,4,1,1,1] => 16

[5,5,2,2,2,1] => 16

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

[5,4,3,2,2,1] => 32

[5,3,3,3,2,1] => 24

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

[4,4,4,3,1,1] => 12

[4,4,4,2,2,1] => 12

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

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

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

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

[4,4,4,3,2,1] => 16

[5,4,3,3,2,1] => 32

[6,3,3,3,2,1] => 32

[6,5,2,2,2,1] => 32

[5,5,3,3,1,1] => 18

[6,5,4,1,1,1] => 32

[5,5,3,3,2] => 18

[5,5,4,2,2] => 18

[6,4,4,2,2] => 27

[6,5,4,3] => 32

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

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

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

[6,4,4,4] => 15

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

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

[18] => 19

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

[6,6,6] => 7

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

[10,4,4] => 35

[9,6,3] => 64

[8,6,4] => 45

[10,8] => 27

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

[9,9] => 10

[7,7,1,1,1,1] => 14

[5,4,4,3,2,1] => 32

[5,5,3,3,2,1] => 24

[5,5,4,2,2,1] => 24

[6,4,4,2,2,1] => 36

[5,5,4,3,1,1] => 24

[6,4,4,3,1,1] => 36

[6,5,3,3,1,1] => 36

[5,5,4,3,2] => 24

[6,4,4,3,2] => 36

[6,5,3,3,2] => 36

[6,5,4,2,2] => 36

[6,5,4,3,1] => 48

[6,5,4,1,1,1,1] => 32

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

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

[19] => 20

[7,2,2,2,2,2,2] => 18

[7,6,6] => 14

[5,2,2,2,2,2,2,2] => 12

[13,6] => 56

[11,4,4] => 40

[9,6,4] => 60

[8,5,4,2] => 72

[8,5,5,1] => 40

[5,5,4,3,2,1] => 32

[6,4,4,3,2,1] => 48

[6,5,3,3,2,1] => 48

[6,5,4,2,2,1] => 48

[6,5,4,3,1,1] => 48

[6,5,4,3,2] => 48

[6,5,2,2,2,2,1] => 32

[6,5,4,2,1,1,1] => 48

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

[7,5,4,3,1] => 72

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

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

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

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

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

[20] => 21

[10,10] => 11

[8,2,2,2,2,2,2] => 21

[8,6,4,2] => 81

[8,6,6] => 21

[10,6,4] => 75

[9,8,3] => 48

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

[10,7,3] => 80

[9,7,4] => 60

[9,5,5,1] => 50

[6,5,4,3,2,1] => 64

[6,3,3,3,3,2,1] => 32

[6,5,3,2,2,2,1] => 48

[6,5,4,3,1,1,1] => 48

[7,6,2,2,2,2] => 30

[6,6,5,4] => 20

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

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

[21] => 22

[11,7,3] => 100

[5,4,2,2,2,2,2,2] => 18

[11,10] => 22

[13,4,4] => 50

[7,6,6,2] => 30

[4,4,4,4,3,2,1] => 16

[6,4,3,3,3,2,1] => 48

[6,5,4,2,2,2,1] => 48

[6,5,4,3,2,1,1] => 64

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

[8,6,2,2,2,2] => 45

[22] => 23

[9,6,4,3] => 96

[8,7,7] => 16

[5,4,4,4,3,2,1] => 32

[6,5,3,3,3,2,1] => 48

[6,5,4,3,2,2,1] => 64

[15,2,2,2,2] => 42

[9,6,5,3] => 96

[8,6,5,3,1] => 108

[6,4,4,4,3,2,1] => 48

[6,5,4,3,3,2,1] => 64

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

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

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

[24] => 25

[11,7,5,1] => 150

[9,7,5,3] => 108

[8,8,8] => 9

[17,7] => 88

[12,9,3] => 112

[5,5,5,4,3,2,1] => 32

[6,5,4,4,3,2,1] => 64

[7,6,6,6] => 14

[5,4,4,4,2,2,2,2] => 18

[13,12] => 26

[15,5,5] => 66

[9,7,5,3,1] => 162

[10,7,5,3] => 144

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

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

[12,10,3] => 96

[6,5,5,4,3,2,1] => 64

[6,6,4,3,3,2,2] => 36

[8,6,6,6] => 21

[9,7,5,4,1] => 144

[16,8,2] => 189

[6,6,5,4,3,2,1] => 64

[7,6,5,4,3,2] => 96

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

[15,6,6] => 70

[7,6,5,4,3,2,1] => 128

[6,6,6,4,3,3] => 24

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

[7,6,5,4,3,1,1,1] => 96

[10,7,6,4,1] => 192

[9,7,6,4,2] => 162

[10,8,5,4,1] => 192

[15,14] => 30

[7,6,5,4,3,2,1,1] => 128

[7,6,5,4,2,2,2,1] => 96

[10,8,6,4,1] => 216

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

[15,15] => 16

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

[6,6,6,6,3,3] => 16

[10,10,10] => 11

[9,7,5,5,3,1] => 162

[7,6,5,4,3,2,2,1] => 128

[7,6,5,3,3,3,2,1] => 96

[11,8,6,4,1] => 288

[10,8,6,4,2] => 243

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

[7,6,6,6,6] => 14

[7,6,5,4,3,3,2,1] => 128

[7,6,4,4,4,3,2,1] => 96

[11,8,6,5,1] => 240

[10,10,9,2] => 48

[14,9,8] => 108

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

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

[7,6,5,4,4,3,2,1] => 128

[7,5,5,5,4,3,2,1] => 96

[16,16] => 17

[10,10,10,2] => 27

[16,8,4,2,2] => 405

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

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

[7,6,5,5,4,3,2,1] => 128

[6,6,6,5,4,3,2,1] => 64

[22,7,4] => 320

[12,12,4,3,2] => 108

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

[7,6,6,5,4,3,2,1] => 128

[12,9,7,5,1] => 360

[7,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 18

[7,7,6,5,4,3,2,1] => 128

[13,9,7,5,1] => 450

[18,18] => 19

[24,12] => 169

[11,9,7,5,3,1] => 486

[11,8,7,5,4,1] => 384

[8,7,6,5,4,3,2,1] => 256

[8,7,7,7,7] => 16

[7,6,2,2,2,2,2,2,2,2,2,2,2,2] => 30

[7,6,6,6,6,6] => 14

[8,7,6,5,4,3,2,1,1] => 256

[8,7,6,5,4,3,2,2,1] => 256

[8,7,6,5,4,3,3,2,1] => 256

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

[12,12,12,4] => 45

[8,7,6,5,4,4,3,2,1] => 256

[11,9,7,5,5,3] => 324

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

[14,14,8,4] => 175

[7,6,6,6,2,2,2,2,2,2,2,2] => 30

[8,7,6,5,5,4,3,2,1] => 256

[9,9,9,9,3,3] => 28

[8,7,6,6,5,4,3,2,1] => 256

[10,10,10,5,5,2] => 72

[16,10,8,8] => 189

[26,9,7] => 432

[8,7,7,6,5,4,3,2,1] => 256

[8,8,7,6,5,4,3,2,1] => 256

[18,18,9] => 100

[9,8,7,6,5,4,3,2,1] => 512

[11,9,7,7,5,3,3] => 324

[48] => 49

[7,6,6,6,6,6,6,6] => 14

[22,9,8,5,5] => 672

[6,6,6,6,6,6,6,3,3,2] => 24

[27,14,9] => 840

[17,14,13,8] => 432

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

[27,20,8] => 936

[26,13,7,7,2] => 1764

[31,12,10,4] => 2100

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

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

[12,12,12,12,12] => 13

[12,12,12,12,11,4] => 80

[12,12,12,12,12,4] => 45

[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] => 6

[11,11,11,11,11,10] => 22

[11,11,11,11,11,11] => 12

[16,14,9,9,9,9] => 180

[8,8,8,8,8,8,8,8,4,2] => 45

[24,24,24] => 25

[16,16,16,16,8,4,2] => 405

[12,12,12,12,12,12,4,4] => 45

[22,20,20,12,8] => 1215

[20,20,8,4,4,4,4,4,4,4,4,4] => 325

[33,32,9,9,5] => 1440

[18,18,18,18,18] => 19

[18,18,18,18,9,9] => 100

[6,6,6,6,6,6,6,6,6,6,6,6,6,6,3,3] => 16

[56,17,11,10,5] => 20160

[33,26,23,12,9] => 15360

[22,22,22,10,10,9,4,4] => 780

[22,22,22,10,10,10,4,4] => 455

[12,12,12,12,12,12,12,12,4,3,2] => 108

[24,24,24,24,14] => 165

[76,22,9,6] => 21560

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

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

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

[12,12,12,12,12,12,12,12,12,12] => 13

[24,24,24,24,24] => 25

[12,12,12,12,12,12,12,12,12,6,6,6,4,2] => 189

[54,48,18,10,8] => 52731

[24,24,24,24,24,24] => 25

[37,33,20,20,13,10,10,10,7] => 71680

[42,34,30,22,22,14,2] => 142155

[54,52,34,18,11,7] => 310080

[65,27,27,25,13,9,6,6] => 212940

[18,18,18,18,18,18,18,18,18,18] => 19

[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] => 7

[16,16,16,16,16,16,16,8,8,8,8,8,8,8,8,4,2] => 405

[58,38,38,38,30] => 5859

[12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12] => 13

[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] => 27

[74,58,34,34,22,22,13,11,2] => 4972500

[61,48,48,48,45,22,12,2] => 487872

[15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,5,5,3,3] => 132

[98,62,36,26,14,14,14,14,14,14,12,2] => 14142843

[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] => 72

[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] => 39

[74,74,26,26,26,26,12,12,12,12,12,12,6,6,4,4,3,3,3,3] => 123480

[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] => 7

[64,57,40,39,28,23,19,19,16,9,8,8,8,8,8,8,6,6] => 139345920

[70,70,46,28,22,22,10,9,9,9,9,8,8,8,8,8,7,7,7,3,3,3] => 6916000

[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] => 144

[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] => 168

[145,83,62,44,44,42,19,16,16,10,8] => 1433412288

[98,98,37,37,37,37,24,24,24,24,24,24,24,24,10,10,8,8] => 351540

[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] => 7

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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 1,0,2 1,1,1,1,1 1,0,2,0,3,0,1 1,1,3,0,1,1,2,1,1 1,0,3,0,3,0,4,0,1,0,3 1,1,3,1,3,0,3,2,1,0,4,0,1,1,1 1,0,5,0,3,0,5,0,3,0,6,0,1,0,3,0,2,0,1 1,1,4,0,5,0,7,2,1,1,4,0,1,2,5,0,3,0,2,1,0,0,2

$F_{1} = q^{2}$

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

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

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

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

$F_{6} = q^{2} + q^{3} + 3\ q^{4} + q^{6} + q^{7} + 2\ q^{8} + q^{9} + q^{10}$

$F_{7} = q^{2} + 3\ q^{4} + 3\ q^{6} + 4\ q^{8} + q^{10} + 3\ q^{12}$

$F_{8} = q^{2} + q^{3} + 3\ q^{4} + q^{5} + 3\ q^{6} + 3\ q^{8} + 2\ q^{9} + q^{10} + 4\ q^{12} + q^{14} + q^{15} + q^{16}$

$F_{9} = q^{2} + 5\ q^{4} + 3\ q^{6} + 5\ q^{8} + 3\ q^{10} + 6\ q^{12} + q^{14} + 3\ q^{16} + 2\ q^{18} + q^{20}$

$F_{10} = q^{2} + q^{3} + 4\ q^{4} + 5\ q^{6} + 7\ q^{8} + 2\ q^{9} + q^{10} + q^{11} + 4\ q^{12} + q^{14} + 2\ q^{15} + 5\ q^{16} + 3\ q^{18} + 2\ q^{20} + q^{21} + 2\ q^{24}$

Description

The number of partitions interlacing the given partition.

Code

def statistic(la):
    la = list(la) + [0]
    return prod(la[i] - la[i+1] + 1 for i in range(len(la)-1))

Created

Jul 08, 2022 at 09:24 by Martin Rubey

Updated

Dec 29, 2023 at 11:40 by Martin Rubey

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