Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001457
Mapping
St001457: Plane partitions ⟶ 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]]
 => 2
[[1],[1],[1]]
 => 3
[[2],[1]]
 => 1
[[1,1],[1]]
 => 3
[[3]]
 => 1
[[2,1]]
 => 1
[[1,1,1]]
 => 3
[[1],[1],[1],[1]]
 => 4
[[2],[1],[1]]
 => 2
[[2],[2]]
 => 2
[[1,1],[1],[1]]
 => 4
[[1,1],[1,1]]
 => 4
[[3],[1]]
 => 1
[[2,1],[1]]
 => 2
[[1,1,1],[1]]
 => 4
[[4]]
 => 1
[[3,1]]
 => 1
[[2,2]]
 => 2
[[2,1,1]]
 => 2
[[1,1,1,1]]
 => 4
[[1],[1],[1],[1],[1]]
 => 5
[[2],[1],[1],[1]]
 => 3
[[2],[2],[1]]
 => 1
[[1,1],[1],[1],[1]]
 => 5
[[1,1],[1,1],[1]]
 => 5
[[3],[1],[1]]
 => 2
[[3],[2]]
 => 1
[[2,1],[1],[1]]
 => 3
[[2,1],[2]]
 => 1
[[2,1],[1,1]]
 => 3
[[1,1,1],[1],[1]]
 => 5
[[1,1,1],[1,1]]
 => 5
[[4],[1]]
 => 1
[[3,1],[1]]
 => 2
[[2,2],[1]]
 => 1
[[2,1,1],[1]]
 => 3
[[1,1,1,1],[1]]
 => 5
[[5]]
 => 1
[[4,1]]
 => 1
[[3,2]]
 => 1
[[3,1,1]]
 => 2
[[2,2,1]]
 => 1
[[2,1,1,1]]
 => 3
[[1,1,1,1,1]]
 => 5
[[1],[1],[1],[1],[1],[1]]
 => 6
[[2],[1],[1],[1],[1]]
 => 4
[[2],[2],[1],[1]]
 => 2
Description
Multiplicity of the smallest part of a plane partition.
Matching statistic: St000160
Mapping
Mp00311: Plane partitions —to partition⟶ Integer partitions
Mp00044: Integer partitions —conjugate⟶ Integer partitions
St000160: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[[1]]
 => [1]
 => [1]
 => 1
[[1],[1]]
 => [1,1]
 => [2]
 => 1
[[2]]
 => [2]
 => [1,1]
 => 2
[[1,1]]
 => [2]
 => [1,1]
 => 2
[[1],[1],[1]]
 => [1,1,1]
 => [3]
 => 1
[[2],[1]]
 => [2,1]
 => [2,1]
 => 1
[[1,1],[1]]
 => [2,1]
 => [2,1]
 => 1
[[3]]
 => [3]
 => [1,1,1]
 => 3
[[2,1]]
 => [3]
 => [1,1,1]
 => 3
[[1,1,1]]
 => [3]
 => [1,1,1]
 => 3
[[1],[1],[1],[1]]
 => [1,1,1,1]
 => [4]
 => 1
[[2],[1],[1]]
 => [2,1,1]
 => [3,1]
 => 1
[[2],[2]]
 => [2,2]
 => [2,2]
 => 2
[[1,1],[1],[1]]
 => [2,1,1]
 => [3,1]
 => 1
[[1,1],[1,1]]
 => [2,2]
 => [2,2]
 => 2
[[3],[1]]
 => [3,1]
 => [2,1,1]
 => 2
[[2,1],[1]]
 => [3,1]
 => [2,1,1]
 => 2
[[1,1,1],[1]]
 => [3,1]
 => [2,1,1]
 => 2
[[4]]
 => [4]
 => [1,1,1,1]
 => 4
[[3,1]]
 => [4]
 => [1,1,1,1]
 => 4
[[2,2]]
 => [4]
 => [1,1,1,1]
 => 4
[[2,1,1]]
 => [4]
 => [1,1,1,1]
 => 4
[[1,1,1,1]]
 => [4]
 => [1,1,1,1]
 => 4
[[1],[1],[1],[1],[1]]
 => [1,1,1,1,1]
 => [5]
 => 1
[[2],[1],[1],[1]]
 => [2,1,1,1]
 => [4,1]
 => 1
[[2],[2],[1]]
 => [2,2,1]
 => [3,2]
 => 1
[[1,1],[1],[1],[1]]
 => [2,1,1,1]
 => [4,1]
 => 1
[[1,1],[1,1],[1]]
 => [2,2,1]
 => [3,2]
 => 1
[[3],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => 2
[[3],[2]]
 => [3,2]
 => [2,2,1]
 => 1
[[2,1],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => 2
[[2,1],[2]]
 => [3,2]
 => [2,2,1]
 => 1
[[2,1],[1,1]]
 => [3,2]
 => [2,2,1]
 => 1
[[1,1,1],[1],[1]]
 => [3,1,1]
 => [3,1,1]
 => 2
[[1,1,1],[1,1]]
 => [3,2]
 => [2,2,1]
 => 1
[[4],[1]]
 => [4,1]
 => [2,1,1,1]
 => 3
[[3,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => 3
[[2,2],[1]]
 => [4,1]
 => [2,1,1,1]
 => 3
[[2,1,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => 3
[[1,1,1,1],[1]]
 => [4,1]
 => [2,1,1,1]
 => 3
[[5]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[4,1]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[3,2]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[3,1,1]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[2,2,1]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[2,1,1,1]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[1,1,1,1,1]]
 => [5]
 => [1,1,1,1,1]
 => 5
[[1],[1],[1],[1],[1],[1]]
 => [1,1,1,1,1,1]
 => [6]
 => 1
[[2],[1],[1],[1],[1]]
 => [2,1,1,1,1]
 => [5,1]
 => 1
[[2],[2],[1],[1]]
 => [2,2,1,1]
 => [4,2]
 => 1
Description
The multiplicity of the smallest part of a partition. This counts the number of occurrences of the smallest part $spt(\lambda)$ of a partition $\lambda$. The sum $spt(n) = \sum_{\lambda \vdash n} spt(\lambda)$ satisfies the congruences \begin{align*} spt(5n+4) &\equiv 0\quad \pmod{5}\\\ spt(7n+5) &\equiv 0\quad \pmod{7}\\\ spt(13n+6) &\equiv 0\quad \pmod{13}, \end{align*} analogous to those of the counting function of partitions, see [1] and [2].