%I #8 Jan 14 2019 09:01:42

%S 12,120,840,5178,29772,163878,875592,4578186,23548164,119570574,

%T 600870336,2993807250,14810051580,72819229974,356173467576,

%U 1734202809114,8410141924596,40641730213278,195782548631472,940481337385122

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

%H R. H. Hardin, <a href="/A268634/b268634.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 10*a(n-1) - 29*a(n-2) + 20*a(n-3) - 4*a(n-4).

%F 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 Some solutions for n=6:

%e ..0..0..0. .1..0..0. .1..0..0. .2..1..0. .0..1..2. .1..0..1. .1..0..0

%e ..0..1..1. .0..1..0. .2..1..0. .1..0..0. .1..2..1. .0..1..0. .2..2..1

%e ..0..0..0. .1..2..1. .1..0..0. .2..1..0. .2..2..1. .1..0..0. .2..1..0

%e ..0..0..1. .2..2..2. .2..1..1. .2..0..0. .2..1..0. .2..1..0. .1..2..1

%e ..0..1..0. .2..1..2. .1..2..2. .1..0..1. .1..2..1. .0..0..0. .2..2..2

%e ..1..0..0. .0..0..1. .2..2..2. .2..1..0. .0..1..2. .0..0..0. .1..2..2

%Y Column 3 of A268639.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 09 2016