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Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001610
Mapping
St001610: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 3
[1,1]
 => 4
[3]
 => 7
[2,1]
 => 15
[1,1,1]
 => 27
[4]
 => 19
[3,1]
 => 52
[2,2]
 => 76
[2,1,1]
 => 136
[1,1,1,1]
 => 256
[5]
 => 47
[4,1]
 => 175
[3,2]
 => 316
[3,1,1]
 => 595
[2,2,1]
 => 855
[2,1,1,1]
 => 1630
[1,1,1,1,1]
 => 3125
[6]
 => 130
[5,1]
 => 571
[4,2]
 => 1270
[4,1,1]
 => 2406
[3,3]
 => 1614
[3,2,1]
 => 4465
[3,1,1,1]
 => 8598
[2,2,2]
 => 6489
[2,2,1,1]
 => 12468
[2,1,1,1,1]
 => 24096
[1,1,1,1,1,1]
 => 46656
[7]
 => 343
[6,1]
 => 1838
[5,2]
 => 4790
[5,1,1]
 => 9216
[4,3]
 => 7464
[4,2,1]
 => 20955
[4,1,1,1]
 => 40593
[3,3,1]
 => 27084
[3,2,2]
 => 39467
[3,2,1,1]
 => 76563
[3,1,1,1,1]
 => 148792
[2,2,2,1]
 => 111685
[2,2,1,1,1]
 => 217154
[2,1,1,1,1,1]
 => 422709
[1,1,1,1,1,1,1]
 => 823543
[8]
 => 951
[7,1]
 => 5834
[6,2]
 => 17590
[6,1,1]
 => 34003
[5,3]
 => 32213
[5,2,1]
 => 91369
Description
The number of coloured endofunctions such that the multiplicities of colours are given by a partition. In particular, the value on the partition (n) is the number of endofunctions on n vertices up to relabelling, [[oeis:A000088]], whereas the value on the partition (1n) is the number of endofunctions [[oeis:A000312]].