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%I #11 Aug 02 2018 15:20:09
%S 1,7,30,126,534,2275,9667,41089,174660,742428,3155820,13414405,
%T 57020437,242375995,1030264362,4379330826,18615162402,79127219431,
%U 336345003127,1429697162869,6077194423824,25832248272072,109804788896376
%N Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors.
%C Column 3 of A220725.
%H R. H. Hardin, <a href="/A220720/b220720.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 4*a(n-2) + 5*a(n-3) + 3*a(n-4) - 2*a(n-5).
%F Empirical g.f.: x*(1 + 4*x + 5*x^2 + 3*x^3 - 2*x^4) / ((1 + x)*(1 - 4*x - 5*x^3 + 2*x^4)). - _Colin Barker_, Aug 02 2018
%e Some solutions for n=3 0=self 1=nw 3=ne 4=w 6=e 7=sw 9=se (reciprocal directions total 10):
%e .69.49.00...69.47.00...00.00.00...00.79.00...69.47.00...00.69.47...00.79.00
%e .00.17.17...39.16.47...00.69.47...39.69.14...39.19.00...00.36.14...36.49.17
%e .36.34.00...00.13.00...00.36.14...00.16.14...00.16.14...00.00.00...00.36.14
%Y Cf. A220725.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 18 2012
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