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Number of 2 X n 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.
1

%I #8 Sep 25 2018 12:19:44

%S 0,0,0,4,0,32,80,560,2080,10720,46496,220896,998432,4634272,21207840,

%T 97791904,449099040,2066934176,9501790240,43707407520,200983135008,

%U 924361443232,4250915450400,19549937082016,89907588137248

%N Number of 2 X n 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.

%H R. H. Hardin, <a href="/A231038/b231038.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) + 6*a(n-2) + 32*a(n-4) - 20*a(n-5) + 24*a(n-6) - 16*a(n-7).

%F Empirical g.f.: 4*x^4*(1 - 3*x + 2*x^2 - 4*x^3) / (1 - 3*x - 6*x^2 - 32*x^4 + 20*x^5 - 24*x^6 + 16*x^7). - _Colin Barker_, Sep 25 2018

%e All solutions for n=4:

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

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

%Y Row 2 of A231037.

%K nonn

%O 1,4

%A _R. H. Hardin_, Nov 03 2013