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Number of 2 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
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%I #8 Jan 17 2019 17:20:28

%S 9,60,240,912,3312,11664,40176,136080,454896,1504656,4933872,16061328,

%T 51963120,167226768,535692528,1709114256,5433452784,17218688400,

%U 54411055344,171498136464,539289320688,1692252695952,5299912289520

%N Number of 2 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

%H R. H. Hardin, <a href="/A268972/b268972.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>4.

%F Conjectures from _Colin Barker_, Jan 17 2019: (Start)

%F G.f.: 3*x*(3 - x)*(1 + x - 4*x^2) / (1 - 3*x)^2.

%F a(n) = 16*3^(n-3) * (4*n+3) for n>2.

%F (End)

%e Some solutions for n=4:

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

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

%Y Row 2 of A268971.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 16 2016