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A269278 Number of 3 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

%I A269278 #8 Jan 21 2019 06:22:23
%S A269278 0,1620,46872,1104264,23549400,474819408,9230973192,174918307032,
%T A269278 3252108138552,59583135523968,1078987217468328,19354648265646120,
%U A269278 344454190256524824,6089633274402902448,107049250394211722184
%N A269278 Number of 3 X n 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
%H A269278 R. H. Hardin, <a href="/A269278/b269278.txt">Table of n, a(n) for n = 1..210</a>
%F A269278 Empirical: a(n) = 36*a(n-1) - 378*a(n-2) + 972*a(n-3) - 729*a(n-4) for n>7.
%F A269278 Empirical g.f.: 36*x^2*(45 - 318*x + 812*x^2 - 1698*x^3 + 2061*x^4 - 756*x^5) / (1 - 18*x + 27*x^2)^2. - _Colin Barker_, Jan 21 2019
%e A269278 Some solutions for n=3:
%e A269278 ..2..3..1. .0..1..3. .3..2..1. .2..2..2. .1..0..0. .0..0..3. .2..0..2
%e A269278 ..3..0..2. .3..3..0. .3..3..3. .0..0..1. .2..2..0. .0..1..3. .0..0..1
%e A269278 ..2..0..1. .2..0..1. .2..3..1. .2..0..3. .3..0..1. .3..3..2. .3..3..3
%Y A269278 Row 3 of A269276.
%K A269278 nonn
%O A269278 1,2
%A A269278 _R. H. Hardin_, Feb 21 2016