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A268967 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

%I A268967 #8 Jan 17 2019 09:20:12
%S A268967 60,912,11664,136080,1504656,16061328,167226768,1709114256,
%T A268967 17218688400,171498136464,1692252695952,16569199473552,
%U A268967 161173122151824,1559011041375120,15007175850454416,143849270956794768
%N A268967 Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
%H A268967 R. H. Hardin, <a href="/A268967/b268967.txt">Table of n, a(n) for n = 1..210</a>
%F A268967 Empirical: a(n) = 18*a(n-1) - 81*a(n-2) for n>3.
%F A268967 Conjectures from _Colin Barker_, Jan 17 2019: (Start)
%F A268967 G.f.: 12*x*(1 - x)*(5 - 9*x) / (1 - 9*x)^2.
%F A268967 a(n) = 16*3^(2*n-3) * (8*n+3) for n>1.
%F A268967 (End)
%e A268967 Some solutions for n=4:
%e A268967 ..1..0..0..0. .1..0..1..2. .2..1..0..1. .2..1..2..1. .2..1..2..1
%e A268967 ..1..0..0..1. .0..0..1..2. .0..0..0..0. .2..1..2..2. .2..1..2..2
%e A268967 ..0..1..2..0. .1..0..2..2. .1..2..1..2. .2..2..1..2. .0..0..1..2
%e A268967 ..2..1..0..0. .0..1..2..1. .1..0..1..0. .1..0..1..1. .1..2..1..2
%Y A268967 Column 4 of A268971.
%K A268967 nonn
%O A268967 1,1
%A A268967 _R. H. Hardin_, Feb 16 2016