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%I #8 Feb 24 2019 10:54:22
%S 3,9,21,57,153,393,1041,2745,7185,18921,49761,130713,343761,903753,
%T 2375553,6245625,16419249,43163817,113476065,298319193,784254225,
%U 2061749001,5420172609,14249195961,37460035185,98479462761,258894708897
%N Number of n X 2 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.
%H R. H. Hardin, <a href="/A296719/b296719.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = a(n-1) + 2*a(n-2) + 6*a(n-3).
%F Empirical g.f.: 3*x*(1 + 2*x + 2*x^2) / (1 - x - 2*x^2 - 6*x^3).
%e Some solutions for n=5:
%e ..0..0. .1..0. .1..1. .0..1. .1..0. .0..0. .0..0. .0..1. .0..1. .0..0
%e ..0..1. .1..1. .0..1. .1..1. .1..1. .0..0. .0..0. .1..1. .1..1. .1..1
%e ..0..0. .1..1. .1..1. .1..1. .0..0. .0..0. .1..0. .1..1. .0..0. .1..0
%e ..0..0. .0..1. .0..0. .1..0. .1..1. .0..1. .0..0. .0..1. .0..1. .1..1
%e ..0..1. .0..0. .1..0. .0..0. .0..1. .0..0. .0..1. .1..1. .0..0. .0..0
%Y Column 2 of A296725.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 19 2017
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