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A216800 T(n,k)=Number of permutations of an nXk array with each element moving exactly one horizontally or vertically and without 2-loops.

%I A216800 #6 Jul 22 2025 23:35:51
%S A216800 0,0,0,0,2,0,0,2,2,0,0,6,0,6,0,0,10,8,8,10,0,0,22,0,88,0,22,0,0,42,32,
%T A216800 292,292,32,42,0,0,86,0,1774,0,1774,0,86,0,0,170,128,7676,10140,10140,
%U A216800 7676,128,170,0,0,342,0,39844,0,207408,0,39844,0,342,0,0,682,512,186996
%N A216800 T(n,k)=Number of permutations of an nXk array with each element moving exactly one horizontally or vertically and without 2-loops.
%C A216800 Table starts
%C A216800 .0....0....0........0.........0............0..............0.................0
%C A216800 .0....2....2........6........10...........22.............42................86
%C A216800 .0....2....0........8.........0...........32..............0...............128
%C A216800 .0....6....8.......88.......292.........1774...........7676.............39844
%C A216800 .0...10....0......292.........0........10140..............0............361200
%C A216800 .0...22...32.....1774.....10140.......207408........1879040..........27918806
%C A216800 .0...42....0.....7676.........0......1879040..............0.........489300384
%C A216800 .0...86..128....39844....361200.....27918806......489300384.......22902801416
%C A216800 .0..170....0...186996.........0....302667484..............0......539812977524
%C A216800 .0..342..512...927134..12911864...3991662992...129127695440....20296105418276
%C A216800 .0..682....0..4460016.........0..46492284664..............0...550843711073468
%C A216800 .0.1366.2048.21812696.461788640.585384941184.34175930646380.18708387030790218
%H A216800 R. H. Hardin, <a href="/A216800/b216800.txt">Table of n, a(n) for n = 1..312</a>
%e A216800 Some solutions for n=4 k=4
%e A216800 ..1..5..3..7....1..5..3..7....4..0..1..2....1..5..3..7....4..0..1..2
%e A216800 ..0..9..2..6....0..4..2..6....8..6..7..3....0..4..2..6....5..6..7..3
%e A216800 ..4.13.11.15....9.13.11.15...12..5..9.10...12..8.14.10...12..8..9.10
%e A216800 ..8.12.10.14....8.12.10.14...13.14.15.11...13..9.15.11...13.14.15.11
%Y A216800 Column 2 is A014113(n-1)
%Y A216800 Diagonal is A216678
%K A216800 nonn,tabl
%O A216800 1,5
%A A216800 _R. H. Hardin_ Sep 17 2012