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%I #9 Sep 28 2018 06:57:58
%S 0,2,8,66,400,2722,17688,117026,768800,5064642,33328168,219411586,
%T 1444225200,9506897762,62579419448,411934939746,2711589889600,
%U 17849253534082,117494042259528,773413479117506,5091052634882000
%N Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero.
%H R. H. Hardin, <a href="/A231280/b231280.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 4*a(n-1) + 17*a(n-2).
%F Conjectures from _Colin Barker_, Sep 28 2018: (Start)
%F G.f.: 2*x^2 / (1 - 4*x - 17*x^2).
%F a(n) = ((2-sqrt(21))^n*(2+sqrt(21)) + (-2+sqrt(21))*(2+sqrt(21))^n)/(17*sqrt(21)).
%F (End)
%e Some solutions for n=3:
%e ..0..1..0....0..1..2....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0
%e ..2..3..2....0..3..0....2..3..0....2..3..0....0..3..2....2..3..2....2..3..2
%e ..0..1..0....2..1..0....2..1..0....2..1..0....2..1..0....0..1..0....2..1..0
%Y Column 3 of A231285.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 06 2013