Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000818
Mapping
St000818: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,1] => 1
[2] => 2
[1,1,1] => 1
[1,2] => 2
[2,1] => 2
[3] => 4
[1,1,1,1] => 1
[1,1,2] => 2
[1,2,1] => 2
[1,3] => 8
[2,1,1] => 2
[2,2] => 6
[3,1] => 4
[4] => 8
[1,1,1,1,1] => 1
[1,1,1,2] => 2
[1,1,2,1] => 2
[1,1,3] => 12
[1,2,1,1] => 2
[1,2,2] => 6
[1,3,1] => 8
[1,4] => 24
[2,1,1,1] => 2
[2,1,2] => 4
[2,2,1] => 6
[2,3] => 12
[3,1,1] => 4
[3,2] => 16
[4,1] => 8
[5] => 16
[1,1,1,1,1,1] => 1
[1,1,1,1,2] => 2
[1,1,1,2,1] => 2
[1,1,1,3] => 16
[1,1,2,1,1] => 2
[1,1,2,2] => 6
[1,1,3,1] => 12
[1,1,4] => 48
[1,2,1,1,1] => 2
[1,2,1,2] => 4
[1,2,2,1] => 6
[1,2,3] => 12
[1,3,1,1] => 8
[1,3,2] => 28
[1,4,1] => 24
[1,5] => 64
[2,1,1,1,1] => 2
[2,1,1,2] => 4
[2,1,2,1] => 4
[2,1,3] => 20
Description
The sum of the entries in the column specified by the composition of the change of basis matrix from quasisymmetric Schur functions to monomial quasisymmetric functions. For example, $QS_{31} = M_{1111} + M_{121} + M_{211} + M_{31}$, so the statistic on the composition $31$ is 4. Apparently, the sum over all compositions gives the sequence [[oeis:A138178]].