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%I #8 Aug 01 2018 05:52:15
%S 1,8,33,155,710,3265,15009,68992,317149,1457879,6701646,30806405,
%T 141612197,650968960,2992401777,13755599635,63232324870,290669037689,
%U 1336159782873,6142116062912,28234340094485,129788814214207
%N Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors.
%C Column 2 of A220595.
%H R. H. Hardin, <a href="/A220590/b220590.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 7*a(n-2) + 2*a(n-3) - 2*a(n-4).
%F Empirical g.f.: x*(1 + x)*(1 + 4*x - 2*x^2) / (1 - 3*x - 7*x^2 - 2*x^3 + 2*x^4). - _Colin Barker_, Aug 01 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...00.00...00.00...00.00...69.47...68.48...89.00...69.48...00.00...68.48
%e .39.17...69.48...00.78...68.48...39.18...29.27...29.17...00.12...69.47...28.28
%e .36.14...00.12...36.24...26.24...00.12...36.14...36.14...00.00...36.14...26.24
%Y Cf. A220595.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 16 2012
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