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Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
1

%I #11 Jan 20 2019 23:18:07

%S 4,108,1620,20412,236196,2598156,27634932,286978140,2927177028,

%T 29443957164,292889889684,2887057484028,28242953648100,

%U 274521509459532,2653707924775476,25530500379736476,244598664928443012

%N Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

%H R. H. Hardin, <a href="/A269270/b269270.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 18*a(n-1) - 81*a(n-2).

%F Conjectures from _Colin Barker_, Jan 20 2019: (Start)

%F G.f.: 4*x*(1 + 9*x) / (1 - 9*x)^2.

%F a(n) = 9^(n-1) * (8*n-4).

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A269276.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 21 2016