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Statistic identifier: St001800
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Collection: Dyck paths
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Description: The number of 3-Catalan paths having this Dyck path as first and last coordinate projections.
A 3-Catalan path is a lattice path from $(0,0,0)$ to $(n,n,n)$ consisting of steps $(1,0,0)$, $(0,1,0)$, and $(0,0,1)$ such that for each point $(x,y,z)$ on the path we have $x \geq y \geq z$.
Its first and last coordinate projections, denoted by $D_{xy}$ and $D_{yz}$, are the Dyck paths obtained by projecting the Catalan path onto the $x,y$-plane and the $y,z$-plane, respectively.
For a given Dyck path $D$ this is the number of Catalan paths $C$ such that $D_{xy}(C) = D_{yz}(C) = D$.
If $D$ is of semilength $n$, $r_i(D)$ denotes the number of downsteps between the $i$-th and $(i+1)$-st upstep, and $s_i(D)$ denotes the number of upsteps between the $i$-th and $(i+1)$-st downstep, then this number is given by $\prod\limits_{i=1}^{n-1} \binom{r_i(D) + s_i(D)}{r_i(D)}$.
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References: [1] Archer, K., Graves, C. Pattern-restricted permutations composed of 3-cycles [[MathSciNet:4400005]] [[arXiv:2104.12664]] [[DOI:10.1016/j.disc.2022.112895]]
[2] Archer, K., Gravies, C. A new statistic on Dyck paths for counting 3-dimensional Catalan words [[arXiv:2205.09686]]
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Code:
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Statistic values:
[] => 1
[1,0] => 1
[1,0,1,0] => 2
[1,1,0,0] => 1
[1,0,1,0,1,0] => 4
[1,0,1,1,0,0] => 3
[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] => 8
[1,0,1,0,1,1,0,0] => 6
[1,0,1,1,0,0,1,0] => 9
[1,0,1,1,0,1,0,0] => 3
[1,0,1,1,1,0,0,0] => 4
[1,1,0,0,1,0,1,0] => 6
[1,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,0,1,0] => 3
[1,1,0,1,0,1,0,0] => 2
[1,1,0,1,1,0,0,0] => 1
[1,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,0,0] => 1
[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] => 16
[1,0,1,0,1,0,1,1,0,0] => 12
[1,0,1,0,1,1,0,0,1,0] => 18
[1,0,1,0,1,1,0,1,0,0] => 6
[1,0,1,0,1,1,1,0,0,0] => 8
[1,0,1,1,0,0,1,0,1,0] => 18
[1,0,1,1,0,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,0,1,0,0] => 6
[1,0,1,1,0,1,1,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0] => 16
[1,0,1,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0] => 5
[1,1,0,0,1,0,1,0,1,0] => 12
[1,1,0,0,1,0,1,1,0,0] => 9
[1,1,0,0,1,1,0,0,1,0] => 18
[1,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,0,1,0,0,1,0] => 6
[1,1,0,1,0,1,0,1,0,0] => 4
[1,1,0,1,0,1,1,0,0,0] => 3
[1,1,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0] => 32
[1,0,1,0,1,0,1,0,1,1,0,0] => 24
[1,0,1,0,1,0,1,1,0,0,1,0] => 36
[1,0,1,0,1,0,1,1,0,1,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,0] => 16
[1,0,1,0,1,1,0,0,1,0,1,0] => 36
[1,0,1,0,1,1,0,0,1,1,0,0] => 36
[1,0,1,0,1,1,0,1,0,0,1,0] => 18
[1,0,1,0,1,1,0,1,0,1,0,0] => 12
[1,0,1,0,1,1,0,1,1,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0] => 32
[1,0,1,0,1,1,1,0,0,1,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0] => 10
[1,0,1,1,0,0,1,0,1,0,1,0] => 36
[1,0,1,1,0,0,1,0,1,1,0,0] => 27
[1,0,1,1,0,0,1,1,0,0,1,0] => 54
[1,0,1,1,0,0,1,1,0,1,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,0] => 30
[1,0,1,1,0,1,0,0,1,0,1,0] => 18
[1,0,1,1,0,1,0,0,1,1,0,0] => 18
[1,0,1,1,0,1,0,1,0,0,1,0] => 18
[1,0,1,1,0,1,0,1,0,1,0,0] => 12
[1,0,1,1,0,1,0,1,1,0,0,0] => 9
[1,0,1,1,0,1,1,0,0,0,1,0] => 12
[1,0,1,1,0,1,1,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,1,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0] => 32
[1,0,1,1,1,0,0,0,1,1,0,0] => 40
[1,0,1,1,1,0,0,1,0,0,1,0] => 12
[1,0,1,1,1,0,0,1,0,1,0,0] => 12
[1,0,1,1,1,0,0,1,1,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0] => 16
[1,0,1,1,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,0] => 25
[1,0,1,1,1,1,0,0,0,1,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0] => 6
[1,1,0,0,1,0,1,0,1,0,1,0] => 24
[1,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,0,1,0,1,1,0,0,1,0] => 27
[1,1,0,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,0,1,1,0,0,1,0,1,0] => 36
[1,1,0,0,1,1,0,0,1,1,0,0] => 36
[1,1,0,0,1,1,0,1,0,0,1,0] => 18
[1,1,0,0,1,1,0,1,0,1,0,0] => 12
[1,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => 40
[1,1,0,0,1,1,1,0,0,1,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,1,0,1,0,0,1,0,1,0,1,0] => 12
[1,1,0,1,0,0,1,0,1,1,0,0] => 9
[1,1,0,1,0,0,1,1,0,0,1,0] => 18
[1,1,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0] => 10
[1,1,0,1,0,1,0,0,1,0,1,0] => 12
[1,1,0,1,0,1,0,0,1,1,0,0] => 12
[1,1,0,1,0,1,0,1,0,0,1,0] => 12
[1,1,0,1,0,1,0,1,0,1,0,0] => 8
[1,1,0,1,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,0,0,1,0] => 12
[1,1,0,1,0,1,1,0,0,1,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,1,0,0,0,0] => 4
[1,1,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0] => 3
[1,1,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,1,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,0,0,1,1,0,0,1,0] => 30
[1,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,0,0,1,1,1,0,0,0] => 20
[1,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,0,1,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,1,1,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 64
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 48
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 72
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => 24
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 32
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 72
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 72
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => 36
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => 24
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => 12
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 64
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => 16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => 16
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 20
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 72
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 54
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 108
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => 36
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 60
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => 36
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => 36
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => 36
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => 24
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => 18
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => 24
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => 12
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 64
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 80
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => 24
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => 24
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => 32
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => 16
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => 8
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => 8
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 50
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => 10
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => 10
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => 10
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 12
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 72
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 54
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 81
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => 27
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 36
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 108
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 108
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => 54
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => 36
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => 18
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 120
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => 30
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => 30
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 45
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => 36
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => 27
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => 54
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => 18
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => 30
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => 36
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => 36
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => 36
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => 24
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => 18
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => 36
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => 9
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => 18
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => 12
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => 24
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => 30
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => 24
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => 12
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => 15
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => 3
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => 3
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => 6
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => 3
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 64
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 48
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 120
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => 40
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 80
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => 24
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => 24
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => 36
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => 24
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => 24
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => 16
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => 4
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => 12
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => 32
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => 40
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => 24
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => 24
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => 12
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => 16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => 8
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => 20
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => 4
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => 8
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => 4
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 50
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 75
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => 15
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => 20
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => 20
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => 15
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => 25
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => 10
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => 5
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => 5
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => 5
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 36
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => 6
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => 6
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => 6
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => 6
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 48
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 36
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 54
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => 18
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 24
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 54
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 54
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => 27
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => 18
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => 9
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 48
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => 12
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 15
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 72
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 54
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 108
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => 36
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 60
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => 36
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => 36
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => 36
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => 24
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => 18
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => 24
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => 12
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => 6
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 80
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 100
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => 30
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => 30
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => 40
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => 20
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => 10
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => 10
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 75
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => 15
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => 15
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => 15
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 21
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => 24
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => 18
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => 27
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => 9
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => 12
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => 36
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => 36
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => 18
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => 6
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => 40
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => 10
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => 15
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => 24
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => 18
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => 36
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => 12
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => 20
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => 24
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => 24
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => 24
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => 16
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => 24
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => 12
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => 8
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => 24
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => 30
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => 9
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => 9
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => 3
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => 24
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => 12
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => 6
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => 9
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => 20
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => 4
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => 8
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => 5
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => 12
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => 30
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => 20
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => 6
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => 9
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => 6
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => 4
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => 1
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => 3
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => 1
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => 16
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => 20
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => 12
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => 12
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => 6
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => 2
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => 15
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => 3
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => 6
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => 3
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => 4
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => 15
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => 4
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => 3
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => 10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => 4
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => 2
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => 3
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => 2
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 32
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 24
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 36
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => 12
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 16
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 60
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 60
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => 30
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => 20
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => 10
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 80
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => 20
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => 20
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 35
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => 12
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => 9
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => 6
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => 10
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => 18
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => 18
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => 18
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => 12
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => 24
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => 12
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => 10
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => 3
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => 3
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => 12
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => 6
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => 3
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => 1
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => 16
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => 30
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => 20
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => 12
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => 18
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => 12
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => 12
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => 12
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => 3
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => 9
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => 4
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => 6
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => 6
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => 3
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => 4
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => 4
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => 10
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => 15
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => 3
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => 4
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => 8
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => 6
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => 3
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => 2
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 20
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 15
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 45
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => 15
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 35
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => 6
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => 12
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => 8
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => 10
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => 10
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => 9
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => 9
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => 6
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => 2
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => 1
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => 3
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => 10
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => 15
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => 3
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => 2
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => 1
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => 2
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 12
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 21
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => 4
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => 4
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => 6
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => 2
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 7
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 1
-----------------------------------------------------------------------------
Created: Jun 02, 2022 at 16:14 by Dennis Jahn
-----------------------------------------------------------------------------
Last Updated: Jun 02, 2022 at 18:06 by Dennis Jahn