Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000212
Mapping
St000212: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 1
[2]
 => 0
[1,1]
 => 1
[3]
 => 0
[2,1]
 => 1
[1,1,1]
 => 1
[4]
 => 0
[3,1]
 => 0
[2,2]
 => 1
[2,1,1]
 => 2
[1,1,1,1]
 => 1
[5]
 => 0
[4,1]
 => 0
[3,2]
 => 1
[3,1,1]
 => 1
[2,2,1]
 => 3
[2,1,1,1]
 => 3
[1,1,1,1,1]
 => 1
[6]
 => 0
[5,1]
 => 0
[4,2]
 => 0
[4,1,1]
 => 0
[3,3]
 => 1
[3,2,1]
 => 5
[3,1,1,1]
 => 3
[2,2,2]
 => 2
[2,2,1,1]
 => 6
[2,1,1,1,1]
 => 4
[1,1,1,1,1,1]
 => 1
[7]
 => 0
[6,1]
 => 0
[5,2]
 => 0
[5,1,1]
 => 0
[4,3]
 => 1
[4,2,1]
 => 2
[4,1,1,1]
 => 1
[3,3,1]
 => 5
[3,2,2]
 => 6
[3,2,1,1]
 => 14
[3,1,1,1,1]
 => 6
[2,2,2,1]
 => 8
[2,2,1,1,1]
 => 10
[2,1,1,1,1,1]
 => 5
[1,1,1,1,1,1,1]
 => 1
[8]
 => 0
[7,1]
 => 0
[6,2]
 => 0
[6,1,1]
 => 0
[5,3]
 => 0
[5,2,1]
 => 0
Description
The number of standard Young tableaux for an integer partition such that no two consecutive entries appear in the same row. Summing over all partitions of $n$ yields the sequence $$1, 1, 1, 2, 4, 9, 22, 59, 170, 516, 1658, \dots$$ which is [[oeis:A237770]]. The references in this sequence of the OEIS indicate a connection with Baxter permutations.