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A268966 Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

%I A268966 #8 Jan 17 2019 09:20:23
%S A268966 24,240,2016,15552,114048,808704,5598720,38071296,255301632,
%T A268966 1693052928,11125776384,72559411200,470184984576,3030081011712,
%U A268966 19434312695808,124128835928064,789910774087680,5010291195641856,31686706480545792
%N A268966 Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
%H A268966 R. H. Hardin, <a href="/A268966/b268966.txt">Table of n, a(n) for n = 1..210</a>
%F A268966 Empirical: a(n) = 12*a(n-1) - 36*a(n-2).
%F A268966 Conjectures from _Colin Barker_, Jan 17 2019: (Start)
%F A268966 G.f.: 24*x*(1 - 2*x) / (1 - 6*x)^2.
%F A268966 a(n) = 2^(n+2) * 3^(n-1) * (2*n+1).
%F A268966 (End)
%e A268966 Some solutions for n=4:
%e A268966 ..1..0..0. .0..1..2. .0..2..2. .2..2..2. .0..0..0. .1..2..1. .1..2..2
%e A268966 ..1..1..2. .2..2..2. .1..2..2. .1..2..2. .0..1..0. .2..1..0. .0..1..0
%e A268966 ..2..2..2. .1..2..2. .2..2..2. .1..0..1. .2..0..1. .0..0..1. .0..0..1
%e A268966 ..2..2..2. .2..1..0. .2..2..2. .1..0..0. .1..0..1. .1..2..1. .0..0..0
%Y A268966 Column 3 of A268971.
%K A268966 nonn
%O A268966 1,1
%A A268966 _R. H. Hardin_, Feb 16 2016