Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001943
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Mapping
St001943: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 5
[1,1]
 => 5
[3]
 => 14
[2,1]
 => 11
[1,1,1]
 => 14
[4]
 => 30
[3,1]
 => 22
[2,2]
 => 18
[2,1,1]
 => 22
[1,1,1,1]
 => 30
[5]
 => 55
[4,1]
 => 40
[3,2]
 => 31
[3,1,1]
 => 35
[2,2,1]
 => 31
[2,1,1,1]
 => 40
[1,1,1,1,1]
 => 55
[6]
 => 91
[5,1]
 => 67
[4,2]
 => 51
[4,1,1]
 => 55
[3,3]
 => 43
[3,2,1]
 => 46
[3,1,1,1]
 => 55
[2,2,2]
 => 43
[2,2,1,1]
 => 51
[2,1,1,1,1]
 => 67
[1,1,1,1,1,1]
 => 91
[7]
 => 140
[6,1]
 => 105
[5,2]
 => 80
[5,1,1]
 => 84
[4,3]
 => 65
[4,2,1]
 => 68
[4,1,1,1]
 => 77
[3,3,1]
 => 60
[3,2,2]
 => 60
[3,2,1,1]
 => 68
[3,1,1,1,1]
 => 84
[2,2,2,1]
 => 65
[2,2,1,1,1]
 => 80
[2,1,1,1,1,1]
 => 105
[1,1,1,1,1,1,1]
 => 140
[8]
 => 204
[7,1]
 => 156
[6,2]
 => 120
[6,1,1]
 => 124
[5,3]
 => 96
[5,2,1]
 => 99
Description
The sum of the squares 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.