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A269271 Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

%I A269271 #10 Jan 20 2019 23:18:00
%S A269271 24,1368,46872,1365336,36673560,938176344,23230366488,561939624792,
%T A269271 13356872620056,313173275509080,7262896745936664,166932248829835608,
%U A269271 3808216985895026712,86327991673633618776,1946351959512905208600
%N A269271 Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
%H A269271 R. H. Hardin, <a href="/A269271/b269271.txt">Table of n, a(n) for n = 1..210</a>
%F A269271 Empirical: a(n) = 42*a(n-1) - 441*a(n-2).
%F A269271 Conjectures from _Colin Barker_, Jan 20 2019: (Start)
%F A269271 G.f.: 24*x*(1 + 15*x) / (1 - 21*x)^2.
%F A269271 a(n) = 8*3^n * 7^(n-2) * (12*n-5).
%F A269271 (End)
%e A269271 Some solutions for n=3:
%e A269271 ..0..0..1. .0..0..1. .0..2..2. .2..0..3. .1..2..0. .3..3..2. .2..3..2
%e A269271 ..0..1..3. .0..2..2. .3..1..0. .1..1..3. .0..0..1. .0..2..2. .0..0..1
%e A269271 ..2..2..0. .2..0..0. .1..1..3. .0..1..0. .0..0..1. .2..2..3. .1..3..3
%Y A269271 Column 3 of A269276.
%K A269271 nonn
%O A269271 1,1
%A A269271 _R. H. Hardin_, Feb 21 2016