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%I #4 Dec 17 2012 10:58:05
%S 1,1,1,1,4,1,1,23,23,1,1,83,333,83,1,1,344,4352,4352,344,1,1,1441,
%T 59846,192413,59846,1441,1,1,5881,816159,8627817,8627817,816159,5881,
%U 1,1,24220,11131560,389859889,1233993907,389859889,11131560,24220,1,1,99767
%N T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two king-move neighbors, without 3-loops
%C Table starts
%C .1.......1...........1..............1................1.................1
%C .1.......4..........23.............83..............344..............1441
%C .1......23.........333...........4352............59846............816159
%C .1......83........4352.........192413..........8627817.........389859889
%C .1.....344.......59846........8627817.......1233993907......179768901595
%C .1....1441......816159......389859889.....179768901595....85240331175084
%C .1....5881....11131560....17592276986...26120030149221.40274546959211319
%C .1...24220...151872860...793772500717.3794284713986274
%C .1...99767..2071881506.35817153012658
%C .1..410363.28265332768
%C .1.1688864
%C .1
%H R. H. Hardin, <a href="/A220652/b220652.txt">Table of n, a(n) for n = 1..84</a>
%e Some solutions for n=3 k=4 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)
%e .00.00.78.78...69.47.00.78...69.47.68.48...00.78.69.47...68.48.79.00
%e .69.34.23.27...36.14.37.28...38.16.24.28...39.28.38.17...29.23.79.18
%e .00.16.34.00...00.36.46.24...26.46.46.24...00.12.23.00...00.13.00.12
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_ Dec 17 2012
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