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A220648 Number of ways to reciprocally link elements of an nX3 array either to themselves or to exactly two king-move neighbors, without 3-loops 1

%I #4 Dec 17 2012 10:55:01

%S 1,23,333,4352,59846,816159,11131560,151872860,2071881506,28265332768,

%T 385605987981,5260573865475,71766627731228,979065962496791,

%U 13356767420074715,182217790214391903,2485880154961341585

%N Number of ways to reciprocally link elements of an nX3 array either to themselves or to exactly two king-move neighbors, without 3-loops

%C Column 3 of A220652

%H R. H. Hardin, <a href="/A220648/b220648.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) +55*a(n-2) +119*a(n-3) -44*a(n-4) -388*a(n-5) -58*a(n-6) +355*a(n-7) +79*a(n-8) -85*a(n-9) -13*a(n-10)

%e Some solutions for n=3 0=self 1=nw 2=n 3=ne 4=w 6=e 7=sw 8=s 9=se (reciprocal directions total 10)

%e .00.67.48...00.69.47...00.89.00...68.46.47...00.00.00...00.67.48...89.67.47

%e .39.89.28...69.34.17...89.27.18...29.36.47...00.67.48...36.47.27...23.13.00

%e .00.12.12...00.13.00...23.16.24...00.13.00...36.46.24...36.34.00...00.00.00

%K nonn

%O 1,2

%A _R. H. Hardin_ Dec 17 2012

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