Identifier
Values
[1] => [1] => 1
[2] => [1,1] => 3
[1,1] => [2] => 3
[3] => [1,1,1] => 6
[2,1] => [2,1] => 5
[1,1,1] => [3] => 6
[4] => [1,1,1,1] => 10
[3,1] => [2,1,1] => 8
[2,2] => [2,2] => 8
[2,1,1] => [3,1] => 8
[1,1,1,1] => [4] => 10
[5] => [1,1,1,1,1] => 15
[4,1] => [2,1,1,1] => 12
[3,2] => [2,2,1] => 11
[3,1,1] => [3,1,1] => 11
[2,2,1] => [3,2] => 11
[2,1,1,1] => [4,1] => 12
[1,1,1,1,1] => [5] => 15
[6] => [1,1,1,1,1,1] => 21
[5,1] => [2,1,1,1,1] => 17
[4,2] => [2,2,1,1] => 15
[4,1,1] => [3,1,1,1] => 15
[3,3] => [2,2,2] => 15
[3,2,1] => [3,2,1] => 14
[3,1,1,1] => [4,1,1] => 15
[2,2,2] => [3,3] => 15
[2,2,1,1] => [4,2] => 15
[2,1,1,1,1] => [5,1] => 17
[1,1,1,1,1,1] => [6] => 21
[7] => [1,1,1,1,1,1,1] => 28
[6,1] => [2,1,1,1,1,1] => 23
[5,2] => [2,2,1,1,1] => 20
[5,1,1] => [3,1,1,1,1] => 20
[4,3] => [2,2,2,1] => 19
[4,2,1] => [3,2,1,1] => 18
[4,1,1,1] => [4,1,1,1] => 19
[3,3,1] => [3,2,2] => 18
[3,2,2] => [3,3,1] => 18
[3,2,1,1] => [4,2,1] => 18
[3,1,1,1,1] => [5,1,1] => 20
[2,2,2,1] => [4,3] => 19
[2,2,1,1,1] => [5,2] => 20
[2,1,1,1,1,1] => [6,1] => 23
[1,1,1,1,1,1,1] => [7] => 28
[8] => [1,1,1,1,1,1,1,1] => 36
[7,1] => [2,1,1,1,1,1,1] => 30
[6,2] => [2,2,1,1,1,1] => 26
[6,1,1] => [3,1,1,1,1,1] => 26
[5,3] => [2,2,2,1,1] => 24
[5,2,1] => [3,2,1,1,1] => 23
[5,1,1,1] => [4,1,1,1,1] => 24
[4,4] => [2,2,2,2] => 24
[4,3,1] => [3,2,2,1] => 22
[4,2,2] => [3,3,1,1] => 22
[4,2,1,1] => [4,2,1,1] => 22
[4,1,1,1,1] => [5,1,1,1] => 24
[3,3,2] => [3,3,2] => 22
[3,3,1,1] => [4,2,2] => 22
[3,2,2,1] => [4,3,1] => 22
[3,2,1,1,1] => [5,2,1] => 23
[3,1,1,1,1,1] => [6,1,1] => 26
[2,2,2,2] => [4,4] => 24
[2,2,2,1,1] => [5,3] => 24
[2,2,1,1,1,1] => [6,2] => 26
[2,1,1,1,1,1,1] => [7,1] => 30
[1,1,1,1,1,1,1,1] => [8] => 36
[9] => [1,1,1,1,1,1,1,1,1] => 45
[8,1] => [2,1,1,1,1,1,1,1] => 38
[7,2] => [2,2,1,1,1,1,1] => 33
[7,1,1] => [3,1,1,1,1,1,1] => 33
[6,3] => [2,2,2,1,1,1] => 30
[6,2,1] => [3,2,1,1,1,1] => 29
[6,1,1,1] => [4,1,1,1,1,1] => 30
[5,4] => [2,2,2,2,1] => 29
[5,3,1] => [3,2,2,1,1] => 27
[5,2,2] => [3,3,1,1,1] => 27
[5,2,1,1] => [4,2,1,1,1] => 27
[5,1,1,1,1] => [5,1,1,1,1] => 29
[4,4,1] => [3,2,2,2] => 27
[4,3,2] => [3,3,2,1] => 26
[4,3,1,1] => [4,2,2,1] => 26
[4,2,2,1] => [4,3,1,1] => 26
[4,2,1,1,1] => [5,2,1,1] => 27
[4,1,1,1,1,1] => [6,1,1,1] => 30
[3,3,3] => [3,3,3] => 27
[3,3,2,1] => [4,3,2] => 26
[3,3,1,1,1] => [5,2,2] => 27
[3,2,2,2] => [4,4,1] => 27
[3,2,2,1,1] => [5,3,1] => 27
[3,2,1,1,1,1] => [6,2,1] => 29
[3,1,1,1,1,1,1] => [7,1,1] => 33
[2,2,2,2,1] => [5,4] => 29
[2,2,2,1,1,1] => [6,3] => 30
[2,2,1,1,1,1,1] => [7,2] => 33
[2,1,1,1,1,1,1,1] => [8,1] => 38
[1,1,1,1,1,1,1,1,1] => [9] => 45
[10] => [1,1,1,1,1,1,1,1,1,1] => 55
[9,1] => [2,1,1,1,1,1,1,1,1] => 47
[8,2] => [2,2,1,1,1,1,1,1] => 41
[8,1,1] => [3,1,1,1,1,1,1,1] => 41
[7,3] => [2,2,2,1,1,1,1] => 37
>>> Load all 576 entries. <<<
[7,2,1] => [3,2,1,1,1,1,1] => 36
[7,1,1,1] => [4,1,1,1,1,1,1] => 37
[6,4] => [2,2,2,2,1,1] => 35
[6,3,1] => [3,2,2,1,1,1] => 33
[6,2,2] => [3,3,1,1,1,1] => 33
[6,2,1,1] => [4,2,1,1,1,1] => 33
[6,1,1,1,1] => [5,1,1,1,1,1] => 35
[5,5] => [2,2,2,2,2] => 35
[5,4,1] => [3,2,2,2,1] => 32
[5,3,2] => [3,3,2,1,1] => 31
[5,3,1,1] => [4,2,2,1,1] => 31
[5,2,2,1] => [4,3,1,1,1] => 31
[5,2,1,1,1] => [5,2,1,1,1] => 32
[5,1,1,1,1,1] => [6,1,1,1,1] => 35
[4,4,2] => [3,3,2,2] => 31
[4,4,1,1] => [4,2,2,2] => 31
[4,3,3] => [3,3,3,1] => 31
[4,3,2,1] => [4,3,2,1] => 30
[4,3,1,1,1] => [5,2,2,1] => 31
[4,2,2,2] => [4,4,1,1] => 31
[4,2,2,1,1] => [5,3,1,1] => 31
[4,2,1,1,1,1] => [6,2,1,1] => 33
[4,1,1,1,1,1,1] => [7,1,1,1] => 37
[3,3,3,1] => [4,3,3] => 31
[3,3,2,2] => [4,4,2] => 31
[3,3,2,1,1] => [5,3,2] => 31
[3,3,1,1,1,1] => [6,2,2] => 33
[3,2,2,2,1] => [5,4,1] => 32
[3,2,2,1,1,1] => [6,3,1] => 33
[3,2,1,1,1,1,1] => [7,2,1] => 36
[3,1,1,1,1,1,1,1] => [8,1,1] => 41
[2,2,2,2,2] => [5,5] => 35
[2,2,2,2,1,1] => [6,4] => 35
[2,2,2,1,1,1,1] => [7,3] => 37
[2,2,1,1,1,1,1,1] => [8,2] => 41
[2,1,1,1,1,1,1,1,1] => [9,1] => 47
[1,1,1,1,1,1,1,1,1,1] => [10] => 55
[11] => [1,1,1,1,1,1,1,1,1,1,1] => 66
[10,1] => [2,1,1,1,1,1,1,1,1,1] => 57
[9,2] => [2,2,1,1,1,1,1,1,1] => 50
[9,1,1] => [3,1,1,1,1,1,1,1,1] => 50
[8,3] => [2,2,2,1,1,1,1,1] => 45
[8,2,1] => [3,2,1,1,1,1,1,1] => 44
[8,1,1,1] => [4,1,1,1,1,1,1,1] => 45
[7,4] => [2,2,2,2,1,1,1] => 42
[7,3,1] => [3,2,2,1,1,1,1] => 40
[7,2,2] => [3,3,1,1,1,1,1] => 40
[7,2,1,1] => [4,2,1,1,1,1,1] => 40
[7,1,1,1,1] => [5,1,1,1,1,1,1] => 42
[6,5] => [2,2,2,2,2,1] => 41
[6,4,1] => [3,2,2,2,1,1] => 38
[6,3,2] => [3,3,2,1,1,1] => 37
[6,3,1,1] => [4,2,2,1,1,1] => 37
[6,2,2,1] => [4,3,1,1,1,1] => 37
[6,2,1,1,1] => [5,2,1,1,1,1] => 38
[6,1,1,1,1,1] => [6,1,1,1,1,1] => 41
[5,5,1] => [3,2,2,2,2] => 38
[5,4,2] => [3,3,2,2,1] => 36
[5,4,1,1] => [4,2,2,2,1] => 36
[5,3,3] => [3,3,3,1,1] => 36
[5,3,2,1] => [4,3,2,1,1] => 35
[5,3,1,1,1] => [5,2,2,1,1] => 36
[5,2,2,2] => [4,4,1,1,1] => 36
[5,2,2,1,1] => [5,3,1,1,1] => 36
[5,2,1,1,1,1] => [6,2,1,1,1] => 38
[5,1,1,1,1,1,1] => [7,1,1,1,1] => 42
[4,4,3] => [3,3,3,2] => 36
[4,4,2,1] => [4,3,2,2] => 35
[4,4,1,1,1] => [5,2,2,2] => 36
[4,3,3,1] => [4,3,3,1] => 35
[4,3,2,2] => [4,4,2,1] => 35
[4,3,2,1,1] => [5,3,2,1] => 35
[4,3,1,1,1,1] => [6,2,2,1] => 37
[4,2,2,2,1] => [5,4,1,1] => 36
[4,2,2,1,1,1] => [6,3,1,1] => 37
[4,2,1,1,1,1,1] => [7,2,1,1] => 40
[4,1,1,1,1,1,1,1] => [8,1,1,1] => 45
[3,3,3,2] => [4,4,3] => 36
[3,3,3,1,1] => [5,3,3] => 36
[3,3,2,2,1] => [5,4,2] => 36
[3,3,2,1,1,1] => [6,3,2] => 37
[3,3,1,1,1,1,1] => [7,2,2] => 40
[3,2,2,2,2] => [5,5,1] => 38
[3,2,2,2,1,1] => [6,4,1] => 38
[3,2,2,1,1,1,1] => [7,3,1] => 40
[3,2,1,1,1,1,1,1] => [8,2,1] => 44
[3,1,1,1,1,1,1,1,1] => [9,1,1] => 50
[2,2,2,2,2,1] => [6,5] => 41
[2,2,2,2,1,1,1] => [7,4] => 42
[2,2,2,1,1,1,1,1] => [8,3] => 45
[2,2,1,1,1,1,1,1,1] => [9,2] => 50
[2,1,1,1,1,1,1,1,1,1] => [10,1] => 57
[1,1,1,1,1,1,1,1,1,1,1] => [11] => 66
[12] => [1,1,1,1,1,1,1,1,1,1,1,1] => 78
[11,1] => [2,1,1,1,1,1,1,1,1,1,1] => 68
[10,2] => [2,2,1,1,1,1,1,1,1,1] => 60
[10,1,1] => [3,1,1,1,1,1,1,1,1,1] => 60
[9,3] => [2,2,2,1,1,1,1,1,1] => 54
[9,2,1] => [3,2,1,1,1,1,1,1,1] => 53
[9,1,1,1] => [4,1,1,1,1,1,1,1,1] => 54
[8,4] => [2,2,2,2,1,1,1,1] => 50
[8,3,1] => [3,2,2,1,1,1,1,1] => 48
[8,2,2] => [3,3,1,1,1,1,1,1] => 48
[8,2,1,1] => [4,2,1,1,1,1,1,1] => 48
[8,1,1,1,1] => [5,1,1,1,1,1,1,1] => 50
[7,5] => [2,2,2,2,2,1,1] => 48
[7,4,1] => [3,2,2,2,1,1,1] => 45
[7,3,2] => [3,3,2,1,1,1,1] => 44
[7,3,1,1] => [4,2,2,1,1,1,1] => 44
[7,2,2,1] => [4,3,1,1,1,1,1] => 44
[7,2,1,1,1] => [5,2,1,1,1,1,1] => 45
[7,1,1,1,1,1] => [6,1,1,1,1,1,1] => 48
[6,6] => [2,2,2,2,2,2] => 48
[6,5,1] => [3,2,2,2,2,1] => 44
[6,4,2] => [3,3,2,2,1,1] => 42
[6,4,1,1] => [4,2,2,2,1,1] => 42
[6,3,3] => [3,3,3,1,1,1] => 42
[6,3,2,1] => [4,3,2,1,1,1] => 41
[6,3,1,1,1] => [5,2,2,1,1,1] => 42
[6,2,2,2] => [4,4,1,1,1,1] => 42
[6,2,2,1,1] => [5,3,1,1,1,1] => 42
[6,2,1,1,1,1] => [6,2,1,1,1,1] => 44
[6,1,1,1,1,1,1] => [7,1,1,1,1,1] => 48
[5,5,2] => [3,3,2,2,2] => 42
[5,5,1,1] => [4,2,2,2,2] => 42
[5,4,3] => [3,3,3,2,1] => 41
[5,4,2,1] => [4,3,2,2,1] => 40
[5,4,1,1,1] => [5,2,2,2,1] => 41
[5,3,3,1] => [4,3,3,1,1] => 40
[5,3,2,2] => [4,4,2,1,1] => 40
[5,3,2,1,1] => [5,3,2,1,1] => 40
[5,3,1,1,1,1] => [6,2,2,1,1] => 42
[5,2,2,2,1] => [5,4,1,1,1] => 41
[5,2,2,1,1,1] => [6,3,1,1,1] => 42
[5,2,1,1,1,1,1] => [7,2,1,1,1] => 45
[5,1,1,1,1,1,1,1] => [8,1,1,1,1] => 50
[4,4,4] => [3,3,3,3] => 42
[4,4,3,1] => [4,3,3,2] => 40
[4,4,2,2] => [4,4,2,2] => 40
[4,4,2,1,1] => [5,3,2,2] => 40
[4,4,1,1,1,1] => [6,2,2,2] => 42
[4,3,3,2] => [4,4,3,1] => 40
[4,3,3,1,1] => [5,3,3,1] => 40
[4,3,2,2,1] => [5,4,2,1] => 40
[4,3,2,1,1,1] => [6,3,2,1] => 41
[4,3,1,1,1,1,1] => [7,2,2,1] => 44
[4,2,2,2,2] => [5,5,1,1] => 42
[4,2,2,2,1,1] => [6,4,1,1] => 42
[4,2,2,1,1,1,1] => [7,3,1,1] => 44
[4,2,1,1,1,1,1,1] => [8,2,1,1] => 48
[4,1,1,1,1,1,1,1,1] => [9,1,1,1] => 54
[3,3,3,3] => [4,4,4] => 42
[3,3,3,2,1] => [5,4,3] => 41
[3,3,3,1,1,1] => [6,3,3] => 42
[3,3,2,2,2] => [5,5,2] => 42
[3,3,2,2,1,1] => [6,4,2] => 42
[3,3,2,1,1,1,1] => [7,3,2] => 44
[3,3,1,1,1,1,1,1] => [8,2,2] => 48
[3,2,2,2,2,1] => [6,5,1] => 44
[3,2,2,2,1,1,1] => [7,4,1] => 45
[3,2,2,1,1,1,1,1] => [8,3,1] => 48
[3,2,1,1,1,1,1,1,1] => [9,2,1] => 53
[3,1,1,1,1,1,1,1,1,1] => [10,1,1] => 60
[2,2,2,2,2,2] => [6,6] => 48
[2,2,2,2,2,1,1] => [7,5] => 48
[2,2,2,2,1,1,1,1] => [8,4] => 50
[2,2,2,1,1,1,1,1,1] => [9,3] => 54
[2,2,1,1,1,1,1,1,1,1] => [10,2] => 60
[2,1,1,1,1,1,1,1,1,1,1] => [11,1] => 68
[1,1,1,1,1,1,1,1,1,1,1,1] => [12] => 78
[13] => [1,1,1,1,1,1,1,1,1,1,1,1,1] => 91
[11,1,1] => [3,1,1,1,1,1,1,1,1,1,1] => 71
[9,4] => [2,2,2,2,1,1,1,1,1] => 59
[8,3,2] => [3,3,2,1,1,1,1,1] => 52
[8,2,1,1,1] => [5,2,1,1,1,1,1,1] => 53
[8,1,1,1,1,1] => [6,1,1,1,1,1,1,1] => 56
[7,6] => [2,2,2,2,2,2,1] => 55
[7,5,1] => [3,2,2,2,2,1,1] => 51
[7,4,2] => [3,3,2,2,1,1,1] => 49
[7,3,1,1,1] => [5,2,2,1,1,1,1] => 49
[7,2,2,1,1] => [5,3,1,1,1,1,1] => 49
[6,6,1] => [3,2,2,2,2,2] => 51
[6,5,2] => [3,3,2,2,2,1] => 48
[6,4,3] => [3,3,3,2,1,1] => 47
[6,4,1,1,1] => [5,2,2,2,1,1] => 47
[6,3,2,1,1] => [5,3,2,1,1,1] => 46
[6,3,1,1,1,1] => [6,2,2,1,1,1] => 48
[6,2,2,2,1] => [5,4,1,1,1,1] => 47
[6,2,2,1,1,1] => [6,3,1,1,1,1] => 48
[5,5,3] => [3,3,3,2,2] => 47
[5,4,4] => [3,3,3,3,1] => 47
[5,4,3,1] => [4,3,3,2,1] => 45
[5,4,2,2] => [4,4,2,2,1] => 45
[5,4,2,1,1] => [5,3,2,2,1] => 45
[5,3,3,2] => [4,4,3,1,1] => 45
[5,3,3,1,1] => [5,3,3,1,1] => 45
[5,3,2,2,1] => [5,4,2,1,1] => 45
[4,4,4,1] => [4,3,3,3] => 46
[4,4,3,2] => [4,4,3,2] => 45
[4,4,3,1,1] => [5,3,3,2] => 45
[4,4,2,2,1] => [5,4,2,2] => 45
[4,4,2,1,1,1] => [6,3,2,2] => 46
[4,3,3,3] => [4,4,4,1] => 46
[4,3,3,2,1] => [5,4,3,1] => 45
[4,3,3,1,1,1] => [6,3,3,1] => 46
[4,3,2,2,2] => [5,5,2,1] => 46
[4,3,2,2,1,1] => [6,4,2,1] => 46
[4,3,2,1,1,1,1] => [7,3,2,1] => 48
[4,2,2,2,2,1] => [6,5,1,1] => 48
[4,2,2,2,1,1,1] => [7,4,1,1] => 49
[4,2,2,1,1,1,1,1] => [8,3,1,1] => 52
[3,3,3,3,1] => [5,4,4] => 47
[3,3,3,2,2] => [5,5,3] => 47
[3,3,3,2,1,1] => [6,4,3] => 47
[3,3,3,1,1,1,1] => [7,3,3] => 49
[3,3,2,2,2,1] => [6,5,2] => 48
[3,3,2,2,1,1,1] => [7,4,2] => 49
[3,3,2,1,1,1,1,1] => [8,3,2] => 52
[3,3,1,1,1,1,1,1,1] => [9,2,2] => 57
[3,2,2,2,2,2] => [6,6,1] => 51
[3,2,2,2,2,1,1] => [7,5,1] => 51
[3,2,2,2,1,1,1,1] => [8,4,1] => 53
[2,2,2,2,2,2,1] => [7,6] => 55
[2,2,2,2,2,1,1,1] => [8,5] => 56
[2,2,2,2,1,1,1,1,1] => [9,4] => 59
[2,2,2,1,1,1,1,1,1,1] => [10,3] => 64
[2,1,1,1,1,1,1,1,1,1,1,1] => [12,1] => 80
[1,1,1,1,1,1,1,1,1,1,1,1,1] => [13] => 91
[14] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 105
[10,2,2] => [3,3,1,1,1,1,1,1,1,1] => 67
[9,1,1,1,1,1] => [6,1,1,1,1,1,1,1,1] => 65
[8,5,1] => [3,2,2,2,2,1,1,1] => 59
[8,3,1,1,1] => [5,2,2,1,1,1,1,1] => 57
[8,2,2,1,1] => [5,3,1,1,1,1,1,1] => 57
[7,7] => [2,2,2,2,2,2,2] => 63
[7,3,2,1,1] => [5,3,2,1,1,1,1] => 53
[7,2,2,2,1] => [5,4,1,1,1,1,1] => 54
[6,6,2] => [3,3,2,2,2,2] => 55
[6,5,3] => [3,3,3,2,2,1] => 53
[6,5,2,1] => [4,3,2,2,2,1] => 52
[6,5,1,1,1] => [5,2,2,2,2,1] => 53
[6,4,4] => [3,3,3,3,1,1] => 53
[6,4,2,1,1] => [5,3,2,2,1,1] => 51
[6,3,2,2,1] => [5,4,2,1,1,1] => 51
[6,2,2,2,2] => [5,5,1,1,1,1] => 53
[5,5,4] => [3,3,3,3,2] => 53
[5,5,2,1,1] => [5,3,2,2,2] => 51
[5,5,1,1,1,1] => [6,2,2,2,2] => 53
[5,4,3,2] => [4,4,3,2,1] => 50
[5,4,3,1,1] => [5,3,3,2,1] => 50
[5,4,2,2,1] => [5,4,2,2,1] => 50
[5,3,3,3] => [4,4,4,1,1] => 51
[5,3,3,2,1] => [5,4,3,1,1] => 50
[5,2,2,2,2,1] => [6,5,1,1,1] => 53
[5,2,2,1,1,1,1,1] => [8,3,1,1,1] => 57
[4,4,4,2] => [4,4,3,3] => 51
[4,4,4,1,1] => [5,3,3,3] => 51
[4,4,3,3] => [4,4,4,2] => 51
[4,4,3,2,1] => [5,4,3,2] => 50
[4,4,2,2,1,1] => [6,4,2,2] => 51
[4,3,3,3,1] => [5,4,4,1] => 51
[4,2,2,2,2,2] => [6,6,1,1] => 55
[3,3,3,3,2] => [5,5,4] => 53
[3,3,3,3,1,1] => [6,4,4] => 53
[3,3,3,2,2,1] => [6,5,3] => 53
[3,3,3,2,1,1,1] => [7,4,3] => 54
[3,3,3,1,1,1,1,1] => [8,3,3] => 57
[3,3,2,2,2,2] => [6,6,2] => 55
[3,3,2,2,2,1,1] => [7,5,2] => 55
[3,3,2,2,1,1,1,1] => [8,4,2] => 57
[3,3,1,1,1,1,1,1,1,1] => [10,2,2] => 67
[3,2,2,2,2,2,1] => [7,6,1] => 58
[3,2,2,2,2,1,1,1] => [8,5,1] => 59
[3,2,1,1,1,1,1,1,1,1,1] => [11,2,1] => 74
[3,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1] => 83
[2,2,2,2,2,2,2] => [7,7] => 63
[2,2,2,2,2,2,1,1] => [8,6] => 63
[2,2,2,2,2,1,1,1,1] => [9,5] => 65
[2,2,1,1,1,1,1,1,1,1,1,1] => [12,2] => 83
[2,1,1,1,1,1,1,1,1,1,1,1,1] => [13,1] => 93
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14] => 105
[15] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 120
[9,2,2,1,1] => [5,3,1,1,1,1,1,1,1] => 66
[8,7] => [2,2,2,2,2,2,2,1] => 71
[8,2,2,1,1,1] => [6,3,1,1,1,1,1,1] => 63
[7,4,2,1,1] => [5,3,2,2,1,1,1] => 58
[6,6,3] => [3,3,3,2,2,2] => 60
[6,5,4] => [3,3,3,3,2,1] => 59
[6,5,2,1,1] => [5,3,2,2,2,1] => 57
[6,5,1,1,1,1] => [6,2,2,2,2,1] => 59
[6,3,3,3] => [4,4,4,1,1,1] => 57
[6,3,3,2,1] => [5,4,3,1,1,1] => 56
[6,2,2,2,2,1] => [6,5,1,1,1,1] => 59
[5,5,5] => [3,3,3,3,3] => 60
[5,5,4,1] => [4,3,3,3,2] => 57
[5,4,3,2,1] => [5,4,3,2,1] => 55
[5,4,2,2,2] => [5,5,2,2,1] => 56
[5,3,3,2,1,1] => [6,4,3,1,1] => 56
[4,4,4,3] => [4,4,4,3] => 57
[4,4,4,2,1] => [5,4,3,3] => 56
[4,4,4,1,1,1] => [6,3,3,3] => 57
[4,3,2,1,1,1,1,1,1] => [9,3,2,1] => 65
[3,3,3,3,3] => [5,5,5] => 60
[3,3,3,3,2,1] => [6,5,4] => 59
[3,3,3,2,2,2] => [6,6,3] => 60
[3,3,3,2,2,1,1] => [7,5,3] => 60
[3,3,2,2,2,1,1,1] => [8,5,2] => 63
[3,3,1,1,1,1,1,1,1,1,1] => [11,2,2] => 78
[3,2,2,2,2,1,1,1,1] => [9,5,1] => 68
[2,2,2,2,2,2,2,1] => [8,7] => 71
[2,2,2,2,2,2,1,1,1] => [9,6] => 72
[2,2,2,1,1,1,1,1,1,1,1,1] => [12,3] => 87
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => [14,1] => 107
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15] => 120
[16] => [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 136
[12,4] => [2,2,2,2,1,1,1,1,1,1,1,1] => 92
[10,6] => [2,2,2,2,2,2,1,1,1,1] => 82
[8,8] => [2,2,2,2,2,2,2,2] => 80
[8,4,4] => [3,3,3,3,1,1,1,1] => 68
[7,7,2] => [3,3,2,2,2,2,2] => 70
[6,6,4] => [3,3,3,3,2,2] => 66
[6,6,2,2] => [4,4,2,2,2,2] => 64
[6,5,4,1] => [4,3,3,3,2,1] => 63
[6,5,2,2,1] => [5,4,2,2,2,1] => 62
[6,4,3,2,1] => [5,4,3,2,1,1] => 61
[5,5,5,1] => [4,3,3,3,3] => 64
[5,5,4,2] => [4,4,3,3,2] => 62
[5,5,3,3] => [4,4,4,2,2] => 62
[5,5,2,2,2] => [5,5,2,2,2] => 62
[5,4,3,1,1,1,1] => [7,3,3,2,1] => 63
[5,1,1,1,1,1,1,1,1,1,1,1] => [12,1,1,1,1] => 92
[4,4,4,4] => [4,4,4,4] => 64
[4,4,4,3,1] => [5,4,4,3] => 62
[4,4,4,2,2] => [5,5,3,3] => 62
[4,4,4,2,1,1] => [6,4,3,3] => 62
[4,4,2,2,2,2] => [6,6,2,2] => 64
[4,3,3,2,2,1,1] => [7,5,3,1] => 64
[3,3,3,3,3,1] => [6,5,5] => 66
[3,3,3,3,2,2] => [6,6,4] => 66
[3,3,3,2,2,2,1] => [7,6,3] => 67
[3,3,3,2,2,1,1,1] => [8,5,3] => 68
[3,3,2,2,2,2,1,1] => [8,6,2] => 70
[2,2,2,2,2,2,2,2] => [8,8] => 80
[2,2,2,2,2,2,1,1,1,1] => [10,6] => 82
[2,2,2,2,1,1,1,1,1,1,1,1] => [12,4] => 92
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [15,1] => 122
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16] => 136
[15,1,1] => [3,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 125
[8,8,1] => [3,2,2,2,2,2,2,2] => 83
[6,6,5] => [3,3,3,3,3,2] => 73
[6,5,4,1,1] => [5,3,3,3,2,1] => 68
[6,5,3,3] => [4,4,4,2,2,1] => 68
[6,5,3,2,1] => [5,4,3,2,2,1] => 67
[6,5,2,2,2] => [5,5,2,2,2,1] => 68
[6,4,4,3] => [4,4,4,3,1,1] => 68
[6,4,4,1,1,1] => [6,3,3,3,1,1] => 68
[6,3,3,3,2] => [5,5,4,1,1,1] => 68
[6,3,3,3,1,1] => [6,4,4,1,1,1] => 68
[5,5,5,2] => [4,4,3,3,3] => 69
[5,5,4,3] => [4,4,4,3,2] => 68
[5,5,4,1,1,1] => [6,3,3,3,2] => 68
[5,5,2,2,2,1] => [6,5,2,2,2] => 68
[4,4,4,4,1] => [5,4,4,4] => 69
[4,4,4,3,2] => [5,5,4,3] => 68
[4,4,4,3,1,1] => [6,4,4,3] => 68
[4,4,4,2,2,1] => [6,5,3,3] => 68
[4,4,3,2,2,1,1] => [7,5,3,2] => 69
[3,3,3,2,2,2,1,1] => [8,6,3] => 75
[3,2,2,2,2,2,2,2] => [8,8,1] => 83
[2,2,2,2,2,2,2,2,1] => [9,8] => 89
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [16,1] => 138
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => [17] => 153
[] => [] => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => 91
[5,5,4,3,2,1] => [6,5,4,3,2] => 85
[6,4,4,3,2,1] => [6,5,4,3,1,1] => 85
[5,4,4,3,2,1] => [6,5,4,3,1] => 79
[4,4,4,3,2,1] => [6,5,4,3] => 74
[6,5,3,3,2,1] => [6,5,4,2,2,1] => 85
[5,5,3,3,2,1] => [6,5,4,2,2] => 79
[6,3,3,3,2,1] => [6,5,4,1,1,1] => 74
[6,5,4,2,2,1] => [6,5,3,3,2,1] => 85
[5,5,4,2,2,1] => [6,5,3,3,2] => 79
[6,4,4,2,2,1] => [6,5,3,3,1,1] => 79
[6,5,2,2,2,1] => [6,5,2,2,2,1] => 74
[6,5,4,3,1,1] => [6,4,4,3,2,1] => 85
[5,5,4,3,1,1] => [6,4,4,3,2] => 79
[6,4,4,3,1,1] => [6,4,4,3,1,1] => 79
[6,5,3,3,1,1] => [6,4,4,2,2,1] => 79
[5,5,3,3,1,1] => [6,4,4,2,2] => 73
[6,5,4,1,1,1] => [6,3,3,3,2,1] => 74
[6,5,4,3,2] => [5,5,4,3,2,1] => 85
[5,5,4,3,2] => [5,5,4,3,2] => 79
[6,4,4,3,2] => [5,5,4,3,1,1] => 79
[6,5,3,3,2] => [5,5,4,2,2,1] => 79
[5,5,3,3,2] => [5,5,4,2,2] => 73
[6,5,4,2,2] => [5,5,3,3,2,1] => 79
[5,5,4,2,2] => [5,5,3,3,2] => 73
[6,4,4,2,2] => [5,5,3,3,1,1] => 73
[6,5,4,3,1] => [5,4,4,3,2,1] => 79
[6,5,4,2,1] => [5,4,3,3,2,1] => 73
[6,5,4,3] => [4,4,4,3,2,1] => 74
[7,6,5,4,3,2,1] => [7,6,5,4,3,2,1] => 140
[6,6,5,4,3,2,1] => [7,6,5,4,3,2] => 133
[6,6,2,2,2,2,1] => [7,6,2,2,2,2] => 95
[7,6,5,4,3,2] => [6,6,5,4,3,2,1] => 133
[4,4,4,4,3,2] => [6,6,5,4] => 95
[6,6,2,2,2,2] => [6,6,2,2,2,2] => 88
[7,6,5,4,3,1] => [6,5,5,4,3,2,1] => 126
[7,6,5,4,2,1] => [6,5,4,4,3,2,1] => 119
[7,6,5,3,2,1] => [6,5,4,3,3,2,1] => 112
[7,6,4,3,2,1] => [6,5,4,3,2,2,1] => 105
[7,5,4,3,2,1] => [6,5,4,3,2,1,1] => 98
[7,4,4,3,2,1] => [6,5,4,3,1,1,1] => 92
[7,6,3,3,2,1] => [6,5,4,2,2,2,1] => 99
[7,3,3,3,2,1] => [6,5,4,1,1,1,1] => 81
[7,6,5,2,2,1] => [6,5,3,3,3,2,1] => 106
[7,6,2,2,2,1] => [6,5,2,2,2,2,1] => 88
[7,6,5,4,1,1] => [6,4,4,4,3,2,1] => 113
[4,4,4,4,1,1] => [6,4,4,4] => 75
[7,6,5,1,1,1] => [6,3,3,3,3,2,1] => 95
[7,6,5,4,3] => [5,5,5,4,3,2,1] => 120
[4,4,4,4,2] => [5,5,4,4] => 75
[7,6,5,4,1] => [5,4,4,4,3,2,1] => 107
[7,6,5,4] => [4,4,4,4,3,2,1] => 102
[5,5,5,4] => [4,4,4,4,3] => 82
[5,5,4,4] => [4,4,4,4,2] => 75
[2,2,2,2,2,2,2,2,2] => [9,9] => 99
[3,3,3,3,3,3] => [6,6,6] => 81
[3,3,3,3,3,3,3,3] => [8,8,8] => 132
[3,3,3,3,3,3,1] => [7,6,6] => 88
[4,4,4,4,4] => [5,5,5,5] => 90
[4,4,4,4,4,4] => [6,6,6,6] => 120
[5,5,5,5] => [4,4,4,4,4] => 90
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [16,16] => 288
[6,6,6,6] => [4,4,4,4,4,4] => 120
[6,2,2,2,2,2,2] => [7,7,1,1,1,1] => 81
[6,6,6] => [3,3,3,3,3,3] => 81
[10,4,4] => [3,3,3,3,1,1,1,1,1,1] => 87
[10,10] => [2,2,2,2,2,2,2,2,2,2] => 120
[6,6,6,6,6] => [5,5,5,5,5,5] => 165
[6,6,6,4,3,3] => [6,6,6,4,3,3] => 142
[10,10,10,10] => [4,4,4,4,4,4,4,4,4,4] => 280
[5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5] => [24,24,24,24,24] => 1740
[5,5,5,5,5,5,5,5,5,5,5,5] => [12,12,12,12,12] => 510
[15,15] => [2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => 255
[5,5,5,5,5,5] => [6,6,6,6,6] => 165
[15,5,5] => [3,3,3,3,3,1,1,1,1,1,1,1,1,1,1] => 165
[6,6,6,2] => [4,4,3,3,3,3] => 90
[7,7,7] => [3,3,3,3,3,3,3] => 105
[8,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1] => 204
[9,8,7,6,5,4,3,2,1] => [9,8,7,6,5,4,3,2,1] => 285
[8,7,6,5,4,3,2] => [7,7,6,5,4,3,2,1] => 196
[8,7,6,5,4,3,1] => [7,6,6,5,4,3,2,1] => 188
[8,7,6,5,4,2,1] => [7,6,5,5,4,3,2,1] => 180
[8,7,6,5,3,2,1] => [7,6,5,4,4,3,2,1] => 172
[8,7,6,4,3,2,1] => [7,6,5,4,3,3,2,1] => 164
[8,7,5,4,3,2,1] => [7,6,5,4,3,2,2,1] => 156
[8,6,5,4,3,2,1] => [7,6,5,4,3,2,1,1] => 148
[9,8,7,6,5,4,3,2] => [8,8,7,6,5,4,3,2,1] => 276
[8,7,6,5,4,3] => [6,6,6,5,4,3,2,1] => 181
[8,7,6,5,4,1,1] => [7,5,5,5,4,3,2,1] => 173
[8,7,6,5,2,2,1] => [7,6,4,4,4,3,2,1] => 165
[8,7,6,3,3,2,1] => [7,6,5,3,3,3,2,1] => 157
[8,7,4,4,3,2,1] => [7,6,5,4,2,2,2,1] => 149
[8,5,5,4,3,2,1] => [7,6,5,4,3,1,1,1] => 141
[9,7,6,5,4,3,2,1] => [8,7,6,5,4,3,2,1,1] => 213
[2,2,2,2,2,2,2,2,2,2,2,2,2,2,2] => [15,15] => 255
[5,5,5,5,5] => [5,5,5,5,5] => 125
[7,7,1,1,1,1] => [6,2,2,2,2,2,2] => 81
[3,3,3,3,3,3,1,1] => [8,6,6] => 96
[6,6,6,1] => [4,3,3,3,3,3] => 85
[3,3,3,3,2,2,1,1,1,1] => [10,6,4] => 100
[4,4,3,3,2,2,1,1] => [8,6,4,2] => 90
[5,5,4,4,3,3,2,2,1,1] => [10,8,6,4,2] => 165
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Description
The sum of the hook lengths of an integer partition.
For a cell in the Ferrers diagram of a partition, the hook length is given by the number of boxes to its right plus the number of boxes below + 1. This statistic is the sum of all hook lengths of a partition.
Map
conjugate
Description
Return the conjugate partition of the partition.
The conjugate partition of the partition $\lambda$ of $n$ is the partition $\lambda^*$ whose Ferrers diagram is obtained from the diagram of $\lambda$ by interchanging rows with columns.
This is also called the associated partition or the transpose in the literature.