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A268634 Number of n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

%I A268634 #8 Jan 14 2019 09:01:42
%S A268634 12,120,840,5178,29772,163878,875592,4578186,23548164,119570574,
%T A268634 600870336,2993807250,14810051580,72819229974,356173467576,
%U A268634 1734202809114,8410141924596,40641730213278,195782548631472,940481337385122
%N A268634 Number of n X 3 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.
%H A268634 R. H. Hardin, <a href="/A268634/b268634.txt">Table of n, a(n) for n = 1..210</a>
%F A268634 Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).
%F A268634 Empirical g.f.: 6*x*(2 - 2*x^2 + 3*x^3) / (1 - 5*x + 2*x^2)^2. - _Colin Barker_, Jan 14 2019
%e A268634 Some solutions for n=6:
%e A268634 ..0..0..0. .1..0..0. .1..0..0. .2..1..0. .0..1..2. .1..0..1. .1..0..0
%e A268634 ..0..1..1. .0..1..0. .2..1..0. .1..0..0. .1..2..1. .0..1..0. .2..2..1
%e A268634 ..0..0..0. .1..2..1. .1..0..0. .2..1..0. .2..2..1. .1..0..0. .2..1..0
%e A268634 ..0..0..1. .2..2..2. .2..1..1. .2..0..0. .2..1..0. .2..1..0. .1..2..1
%e A268634 ..0..1..0. .2..1..2. .1..2..2. .1..0..1. .1..2..1. .0..0..0. .2..2..2
%e A268634 ..1..0..0. .0..0..1. .2..2..2. .2..1..0. .0..1..2. .0..0..0. .1..2..2
%Y A268634 Column 3 of A268639.
%K A268634 nonn
%O A268634 1,1
%A A268634 _R. H. Hardin_, Feb 09 2016