***************************************************************************** * www.FindStat.org - The Combinatorial Statistic Finder * * * * Copyright (C) 2019 The FindStatCrew * * * * This information is distributed in the hope that it will be useful, * * but WITHOUT ANY WARRANTY; without even the implied warranty of * * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * ***************************************************************************** ----------------------------------------------------------------------------- Statistic identifier: St001800 ----------------------------------------------------------------------------- Collection: Dyck paths ----------------------------------------------------------------------------- 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 $\prod\limits_{i=1}^{n-1} \binom{r_i(D) + s_i(D)}{r_i(D)}$. ----------------------------------------------------------------------------- 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]] ----------------------------------------------------------------------------- Code: ----------------------------------------------------------------------------- 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