Processing math: 100%

Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001607
Mapping
St001607: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 2
[1,1]
 => 2
[3]
 => 4
[2,1]
 => 6
[1,1,1]
 => 8
[4]
 => 11
[3,1]
 => 20
[2,2]
 => 28
[2,1,1]
 => 40
[1,1,1,1]
 => 64
[5]
 => 34
[4,1]
 => 90
[3,2]
 => 148
[3,1,1]
 => 240
[2,2,1]
 => 336
[2,1,1,1]
 => 576
[1,1,1,1,1]
 => 1024
[6]
 => 156
[5,1]
 => 544
[4,2]
 => 1144
[4,1,1]
 => 1992
[3,3]
 => 1408
[3,2,1]
 => 3568
[3,1,1,1]
 => 6528
[2,2,2]
 => 5120
[2,2,1,1]
 => 9344
[2,1,1,1,1]
 => 17408
[1,1,1,1,1,1]
 => 32768
[7]
 => 1044
[6,1]
 => 5096
[5,2]
 => 13128
[5,1,1]
 => 24416
[4,3]
 => 20364
[4,2,1]
 => 55472
[4,1,1,1]
 => 105536
[3,3,1]
 => 71552
[3,2,2]
 => 104160
[3,2,1,1]
 => 199040
[3,1,1,1,1]
 => 382976
[2,2,2,1]
 => 290304
[2,2,1,1,1]
 => 559104
[2,1,1,1,1,1]
 => 1081344
[1,1,1,1,1,1,1]
 => 2097152
Description
The number of coloured graphs such that the multiplicities of colours are given by a partition. In particular, the value on the partition (n) is the number of unlabelled graphs on n vertices, [[oeis:A000088]], whereas the value on the partition (1n) is the number of labelled graphs [[oeis:A006125]].