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%I #7 Aug 02 2018 06:24:20
%S 1,12,94,745,5851,46027,362057,2847943,22401961,176214299,1386105209,
%T 10903131303,85764249269,674623302927,5306600415489,41741825175435,
%U 328342033045001,2582745009614887,20315923985816277,159805465061769263
%N Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.
%C Column 3 of A220688.
%H R. H. Hardin, <a href="/A220683/b220683.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) + 12*a(n-2) + 19*a(n-3) + 16*a(n-4) + 2*a(n-5) for n>6.
%F Empirical g.f.: x*(1 + 6*x + 10*x^2 + 18*x^3 + 9*x^4 + x^5) / ((1 + x)*(1 - 7*x - 5*x^2 - 14*x^3 - 2*x^4)). - _Colin Barker_, Aug 02 2018
%e Some solutions for n=3 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10):
%e .68.46.47...68.47.00...00.67.48...00.00.00...68.47.00...00.67.48...00.78.00
%e .28.36.48...23.67.47...36.47.27...68.46.47...23.67.48...38.68.24...38.26.48
%e .26.46.24...36.34.00...36.34.00...26.34.00...36.46.24...26.24.00...26.46.24
%Y Cf. A220688.
%K nonn
%O 1,2
%A _R. H. Hardin_, Dec 17 2012
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