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Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically, 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 23 2018 09:07:00

%S 0,12,54,432,3108,22428,162504,1175592,8507376,61562808,445491480,

%T 3223753560,23328341064,168813022728,1221597213768,8839956302856,

%U 63969389202792,462907576993032,3349780692313320,24240326242963080

%N Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically, 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="/A230920/b230920.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) + 14*a(n-2) + 16*a(n-3) - 2*a(n-4) + 4*a(n-5).

%F Empirical g.f.: 6*x^2*(1 - x)*(2 + x) / (1 - 5*x - 14*x^2 - 16*x^3 + 2*x^4 - 4*x^5). - _Colin Barker_, Sep 23 2018

%e Some solutions for n=3:

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

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

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

%Y Column 2 of A230926.

%K nonn

%O 1,2

%A _R. H. Hardin_, Nov 01 2013