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%I #7 Aug 02 2018 04:42:20
%S 1,1,3,12,44,158,564,2010,7160,25502,90828,323490,1152128,4103366,
%T 14614356,52049802,185378120,660233966,2351458140,8374842354,
%U 29827443344,106232014742,378350930916,1347516822234,4799252328536,17092790630078
%N Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.
%C Row 3 of A220632.
%H R. H. Hardin, <a href="/A220633/b220633.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) - a(n-2) - 2*a(n-3) for n>5.
%F Empirical g.f.: x*(1 - x - x^2)*(1 - 2*x - x^2) / ((1 - x)*(1 - 3*x - 2*x^2)). - _Colin Barker_, Aug 02 2018
%e All solutions for n=3 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10):
%e .00.00.00...00.67.47...00.00.00
%e .00.67.47...36.34.00...00.00.00
%e .36.34.00...00.00.00...00.00.00
%Y Cf. A220632.
%K nonn
%O 1,3
%A _R. H. Hardin_, Dec 17 2012
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