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%I #7 Jan 15 2019 16:11:26
%S 2,14,84,462,2418,12252,60666,295230,1417452,6732102,31690914,
%T 148080468,687592338,3175567374,14597507076,66827528094,304831251762,
%U 1386004252620,6283722000714,28414577975934,128187044049948,577056144993366
%N Number of n X 3 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
%H R. H. Hardin, <a href="/A268881/b268881.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3) - 9*a(n-4).
%F Empirical g.f.: 2*x*(1 - 2*x)*(1 - x + x^2) / (1 - 5*x + 3*x^2)^2. - _Colin Barker_, Jan 15 2019
%e Some solutions for n=4:
%e ..0..1..0. .0..0..0. .1..0..0. .0..1..0. .0..1..1. .1..0..1. .1..0..0
%e ..0..1..0. .0..1..0. .1..1..0. .0..1..0. .0..0..0. .0..0..0. .1..0..0
%e ..1..0..0. .0..0..1. .0..0..1. .1..0..0. .1..0..0. .1..1..0. .1..1..0
%e ..0..0..1. .0..1..0. .1..0..0. .1..0..1. .1..0..0. .0..0..0. .0..1..0
%Y Column 3 of A268886.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 15 2016
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