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Number of n X 3 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.
1

%I #8 Jan 19 2019 06:42:06

%S 24,1152,31296,715320,15024096,300056400,5795398368,109294975080,

%T 2024660774592,36988673403168,668280340085760,11964667932759960,

%U 212595089870143008,3753382504394332656,65903307050002080672

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

%H R. H. Hardin, <a href="/A269092/b269092.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 36*a(n-1) - 378*a(n-2) + 972*a(n-3) - 729*a(n-4) for n>5.

%F 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 Some solutions for n=3:

%e ..1..1..0. .2..0..0. .0..1..0. .2..0..1. .1..2..3. .1..1..0. .0..0..2

%e ..3..3..1. .0..0..1. .0..0..2. .3..1..1. .3..3..3. .1..3..2. .0..0..2

%e ..0..1..0. .2..2..1. .2..1..0. .1..3..2. .2..3..3. .2..2..3. .1..1..2

%Y Column 3 of A269097.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2016