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A269092 Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.

%I A269092 #8 Jan 19 2019 06:42:06
%S A269092 24,1152,31296,715320,15024096,300056400,5795398368,109294975080,
%T A269092 2024660774592,36988673403168,668280340085760,11964667932759960,
%U A269092 212595089870143008,3753382504394332656,65903307050002080672
%N A269092 Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.
%H A269092 R. H. Hardin, <a href="/A269092/b269092.txt">Table of n, a(n) for n = 1..210</a>
%F A269092 Empirical: a(n) = 36*a(n-1) - 378*a(n-2) + 972*a(n-3) - 729*a(n-4) for n>5.
%F A269092 Empirical g.f.: 24*x*(1 + 12*x - 46*x^2 + 33*x^3 + 9*x^4) / (1 - 18*x + 27*x^2)^2. - _Colin Barker_, Jan 19 2019
%e A269092 Some solutions for n=3:
%e A269092 ..1..1..0. .2..0..0. .0..1..0. .2..0..1. .1..2..3. .1..1..0. .0..0..2
%e A269092 ..3..3..1. .0..0..1. .0..0..2. .3..1..1. .3..3..3. .1..3..2. .0..0..2
%e A269092 ..0..1..0. .2..2..1. .2..1..0. .1..3..2. .2..3..3. .2..2..3. .1..1..2
%Y A269092 Column 3 of A269097.
%K A269092 nonn
%O A269092 1,1
%A A269092 _R. H. Hardin_, Feb 19 2016