Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St001777
Mapping
St001777: Integer compositions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1] => 0
[1,1] => 1
[2] => 0
[1,1,1] => 2
[1,2] => 0
[2,1] => 1
[3] => 0
[1,1,1,1] => 3
[1,1,2] => 1
[1,2,1] => 1
[1,3] => 0
[2,1,1] => 2
[2,2] => 1
[3,1] => 1
[4] => 0
[1,1,1,1,1] => 4
[1,1,1,2] => 2
[1,1,2,1] => 2
[1,1,3] => 1
[1,2,1,1] => 2
[1,2,2] => 1
[1,3,1] => 1
[1,4] => 0
[2,1,1,1] => 3
[2,1,2] => 1
[2,2,1] => 2
[2,3] => 0
[3,1,1] => 2
[3,2] => 1
[4,1] => 1
[5] => 0
[1,1,1,1,1,1] => 5
[1,1,1,1,2] => 3
[1,1,1,2,1] => 3
[1,1,1,3] => 2
[1,1,2,1,1] => 3
[1,1,2,2] => 2
[1,1,3,1] => 2
[1,1,4] => 1
[1,2,1,1,1] => 3
[1,2,1,2] => 1
[1,2,2,1] => 2
[1,2,3] => 0
[1,3,1,1] => 2
[1,3,2] => 1
[1,4,1] => 1
[1,5] => 0
[2,1,1,1,1] => 4
[2,1,1,2] => 2
[2,1,2,1] => 2
Description
The number of weak descents in an integer composition. A weak descent of an integer composition $\alpha=(a_1, \dots, a_n)$ is an index $1\leq i < n$ such that $a_i \geq a_{i+1}$.