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 A220633 Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors. 1

%I

%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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Last modified May 15 18:26 EDT 2021. Contains 343920 sequences. (Running on oeis4.)