Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001102
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Mapping
St001102: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 1
[1,1] => 2
[2] => 1
[1,1,1] => 5
[1,2] => 3
[2,1] => 3
[3] => 1
[1,1,1,1] => 16
[1,1,2] => 10
[1,2,1] => 10
[1,3] => 4
[2,1,1] => 10
[2,2] => 6
[3,1] => 4
[4] => 1
[1,1,1,1,1] => 63
[1,1,1,2] => 40
[1,1,2,1] => 40
[1,1,3] => 17
[1,2,1,1] => 39
[1,2,2] => 24
[1,3,1] => 17
[1,4] => 5
[2,1,1,1] => 39
[2,1,2] => 24
[2,2,1] => 24
[2,3] => 10
[3,1,1] => 17
[3,2] => 10
[4,1] => 5
[5] => 1
[1,1,1,1,1,1] => 296
[1,1,1,1,2] => 188
[1,1,1,2,1] => 188
[1,1,1,3] => 82
[1,1,2,1,1] => 184
[1,1,2,2] => 114
[1,1,3,1] => 82
[1,1,4] => 26
[1,2,1,1,1] => 180
[1,2,1,2] => 112
[1,2,2,1] => 112
[1,2,3] => 48
[1,3,1,1] => 80
[1,3,2] => 48
[1,4,1] => 26
[1,5] => 6
[2,1,1,1,1] => 180
[2,1,1,2] => 112
[2,1,2,1] => 112
Description
The number of words with multiplicities of the letters given by the composition, avoiding the consecutive pattern 132. The total number of words with letter multiplicities given by an integer partition is [[St000048]]. For example, there are twelve words with letters $0,0,1,2$ corresponding to the partition $[2,1,1]$. Two of these contain the pattern $132$: $0,0,2,1$ and $0,2,1,0$. Note that this statistic is not constant on compositions having the same parts. The number of words of length $n$ with letters in an alphabet of size $k$ avoiding the consecutive pattern $132$ is determined in [1].