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A216798 Number of permutations of an nX6 array with each element moving exactly one horizontally or vertically and without 2-loops.

%I A216798 #6 Jul 22 2025 23:35:44
%S A216798 0,22,32,1774,10140,207408,1879040,27918806,302667484,3991662992,
%T A216798 46492284664,585384941184,7016484369112,86745644666352,
%U A216798 1051690689056356,12908451995027824,157213197102215752,1924102649175445120
%N A216798 Number of permutations of an nX6 array with each element moving exactly one horizontally or vertically and without 2-loops.
%C A216798 Column 6 of A216800
%H A216798 R. H. Hardin, <a href="/A216798/b216798.txt">Table of n, a(n) for n = 1..210</a>
%F A216798 Empirical: a(n) = 9*a(n-1) +126*a(n-2) -895*a(n-3) -4784*a(n-4) +31216*a(n-5) +75941*a(n-6) -508196*a(n-7) -548324*a(n-8) +4278056*a(n-9) +1798234*a(n-10) -19820128*a(n-11) -2095562*a(n-12) +51982908*a(n-13) -985124*a(n-14) -76511412*a(n-15) +2082320*a(n-16) +59525536*a(n-17) +1713536*a(n-18) -20262336*a(n-19) -1935616*a(n-20) +1498112*a(n-21) +94208*a(n-22) -32768*a(n-23)
%e A216798 Some solutions for n=4
%e A216798 ..6..0..3..9..5.11....1..7..3..4..5.11....6..0..1..9..3..4....6..0..1..2..3..4
%e A216798 .12..1..2..8..4.10....0..6..2..8..9.10....7..8..2.10.16..5...12.13..7.10.16..5
%e A216798 .18..7.13.14.15.16...13.19.15.21.22.16...18.12.20.14.22.11...18.14..8..9.15.11
%e A216798 .19.20.21.22.23.17...12.18.14.20.23.17...19.13.21.15.23.17...19.20.21.22.23.17
%K A216798 nonn
%O A216798 1,2
%A A216798 _R. H. Hardin_ Sep 17 2012