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Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links.
1

%I #9 Aug 02 2018 15:19:49

%S 1,8,26,118,463,1930,7843,32209,131698,539466,2208130,9041065,

%T 37013388,151537869,620403077,2539982216,10398860814,42573713750,

%U 174299854287,713596365222,2921515440791,11960897338493,48968785309970

%N Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors, without consecutive collinear links.

%C Column 2 of A220718.

%H R. H. Hardin, <a href="/A220713/b220713.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 8*a(n-2) + 3*a(n-3) - 2*a(n-4) - 3*a(n-5) + a(n-6).

%F Empirical g.f.: x*(1 + 6*x + 2*x^2 - x^3 - 3*x^4 + x^5) / (1 - 2*x - 8*x^2 - 3*x^3 + 2*x^4 + 3*x^5 - x^6). - _Colin Barker_, Aug 02 2018

%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 .69.47...68.47...89.00...00.00...00.00...00.00...00.78...69.48...00.00...89.78

%e .36.14...23.00...29.17...69.47...68.48...00.78...39.27...00.12...68.47...23.12

%e .00.00...00.00...36.14...36.14...26.24...36.24...36.14...00.00...23.00...00.00

%Y Cf. A220718.

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 18 2012