Your data matches 1 statistic following compositions of up to 3 maps.
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Matching statistic: St000978
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Mapping
St000978: 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]
 => 3
[1,0,1,0,1,0]
 => 0
[1,0,1,1,0,0]
 => 5
[1,1,0,0,1,0]
 => 3
[1,1,0,1,0,0]
 => 5
[1,1,1,0,0,0]
 => 9
[1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,1,0,0]
 => 7
[1,0,1,1,0,0,1,0]
 => 5
[1,0,1,1,0,1,0,0]
 => 7
[1,0,1,1,1,0,0,0]
 => 13
[1,1,0,0,1,0,1,0]
 => 3
[1,1,0,0,1,1,0,0]
 => 10
[1,1,0,1,0,0,1,0]
 => 5
[1,1,0,1,0,1,0,0]
 => 7
[1,1,0,1,1,0,0,0]
 => 13
[1,1,1,0,0,0,1,0]
 => 9
[1,1,1,0,0,1,0,0]
 => 11
[1,1,1,0,1,0,0,0]
 => 13
[1,1,1,1,0,0,0,0]
 => 18
[1,0,1,0,1,0,1,0,1,0]
 => 0
[1,0,1,0,1,0,1,1,0,0]
 => 9
[1,0,1,0,1,1,0,0,1,0]
 => 7
[1,0,1,0,1,1,0,1,0,0]
 => 9
[1,0,1,0,1,1,1,0,0,0]
 => 17
[1,0,1,1,0,0,1,0,1,0]
 => 5
[1,0,1,1,0,0,1,1,0,0]
 => 14
[1,0,1,1,0,1,0,0,1,0]
 => 7
[1,0,1,1,0,1,0,1,0,0]
 => 9
[1,0,1,1,0,1,1,0,0,0]
 => 17
[1,0,1,1,1,0,0,0,1,0]
 => 13
[1,0,1,1,1,0,0,1,0,0]
 => 15
[1,0,1,1,1,0,1,0,0,0]
 => 17
[1,0,1,1,1,1,0,0,0,0]
 => 24
[1,1,0,0,1,0,1,0,1,0]
 => 3
[1,1,0,0,1,0,1,1,0,0]
 => 12
[1,1,0,0,1,1,0,0,1,0]
 => 10
[1,1,0,0,1,1,0,1,0,0]
 => 12
[1,1,0,0,1,1,1,0,0,0]
 => 20
[1,1,0,1,0,0,1,0,1,0]
 => 5
[1,1,0,1,0,0,1,1,0,0]
 => 14
[1,1,0,1,0,1,0,0,1,0]
 => 7
[1,1,0,1,0,1,0,1,0,0]
 => 9
[1,1,0,1,0,1,1,0,0,0]
 => 17
[1,1,0,1,1,0,0,0,1,0]
 => 13
[1,1,0,1,1,0,0,1,0,0]
 => 15
[1,1,0,1,1,0,1,0,0,0]
 => 17
[1,1,0,1,1,1,0,0,0,0]
 => 24
[1,1,1,0,0,0,1,0,1,0]
 => 9
Description
The sum of the positions of double down-steps of a Dyck path. This is part of MacMahon's equal index of a word, see [1, p. 135].