Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000946
Mapping
St000946: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => 0
[1,1,0,0]
 => 1
[1,0,1,0,1,0]
 => 0
[1,0,1,1,0,0]
 => 2
[1,1,0,0,1,0]
 => 3
[1,1,0,1,0,0]
 => 1
[1,1,1,0,0,0]
 => 1
[1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0]
 => 3
[1,0,1,1,0,0,1,0]
 => 5
[1,0,1,1,0,1,0,0]
 => 2
[1,0,1,1,1,0,0,0]
 => 2
[1,1,0,0,1,0,1,0]
 => 3
[1,1,0,0,1,1,0,0]
 => 6
[1,1,0,1,0,0,1,0]
 => 4
[1,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,1,0,0,0]
 => 3
[1,1,1,0,0,0,1,0]
 => 4
[1,1,1,0,0,1,0,0]
 => 3
[1,1,1,0,1,0,0,0]
 => 1
[1,1,1,1,0,0,0,0]
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,0,1,1,0,0]
 => 4
[1,0,1,0,1,1,0,0,1,0]
 => 7
[1,0,1,0,1,1,0,1,0,0]
 => 3
[1,0,1,0,1,1,1,0,0,0]
 => 3
[1,0,1,1,0,0,1,0,1,0]
 => 5
[1,0,1,1,0,0,1,1,0,0]
 => 9
[1,0,1,1,0,1,0,0,1,0]
 => 6
[1,0,1,1,0,1,0,1,0,0]
 => 2
[1,0,1,1,0,1,1,0,0,0]
 => 5
[1,0,1,1,1,0,0,0,1,0]
 => 6
[1,0,1,1,1,0,0,1,0,0]
 => 5
[1,0,1,1,1,0,1,0,0,0]
 => 2
[1,0,1,1,1,1,0,0,0,0]
 => 2
[1,1,0,0,1,0,1,0,1,0]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => 7
[1,1,0,0,1,1,0,0,1,0]
 => 10
[1,1,0,0,1,1,0,1,0,0]
 => 6
[1,1,0,0,1,1,1,0,0,0]
 => 6
[1,1,0,1,0,0,1,0,1,0]
 => 4
[1,1,0,1,0,0,1,1,0,0]
 => 8
[1,1,0,1,0,1,0,0,1,0]
 => 5
[1,1,0,1,0,1,0,1,0,0]
 => 1
[1,1,0,1,0,1,1,0,0,0]
 => 4
[1,1,0,1,1,0,0,0,1,0]
 => 7
[1,1,0,1,1,0,0,1,0,0]
 => 6
[1,1,0,1,1,0,1,0,0,0]
 => 3
[1,1,0,1,1,1,0,0,0,0]
 => 3
[1,1,1,0,0,0,1,0,1,0]
 => 4
Description
The sum of the skew hook positions in a Dyck path. A skew hook is an occurrence of a down step followed by two up steps or of an up step followed by a down step. Write $U_i$ for the $i$-th up step and $D_j$ for the $j$-th down step in the Dyck path. Then the skew hook set is the set $$H = \{j: U_{i−1} U_i D_j \text{ is a skew hook}\} \cup \{i: D_{i−1} D_i U_j\text{ is a skew hook}\}.$$ This statistic is the sum of all elements in $H$.