%I #9 Mar 17 2018 07:10:13

%S 0,0,2,0,2,12,18,56,170,420,1162,3200,8562,23292,63298,171336,464890,

%T 1261140,3419322,9274000,25152322,68211372,184993778,501712216,

%U 1360654410,3690150660,10007829482,27141578400,73608971282,199630236252

%N Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically 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.

%C Column 2 of A230819.

%H R. H. Hardin, <a href="/A230813/b230813.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: 2*x^3*(1 - 2*x) / (1 - 2*x - x^2 - 4*x^3 + 4*x^4). - _Colin Barker_, Mar 17 2018

%e All solutions for n=5:

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

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

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

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

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

%Y Cf. A230819.

%K nonn

%O 1,3

%A _R. H. Hardin_, Oct 30 2013