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%I #8 Feb 07 2019 08:15:39
%S 0,6,30,198,1230,7734,48510,304422,1910190,11986326,75213150,
%T 471956358,2961486990,18583085814,116607324990,731701311462,
%U 4591365157230,28810436277846,180783102647070,1134399003458118,7118259838467150
%N Number of n X 2 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
%H R. H. Hardin, <a href="/A278008/b278008.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) + 8*a(n-2).
%F Conjectures from _Colin Barker_, Feb 07 2019: (Start)
%F G.f.: 6*x^2 / (1 - 5*x - 8*x^2).
%F a(n) = 2^(-3-n) * ((57-5*sqrt(57))*(5+sqrt(57))^n + (5-sqrt(57))^n*(57+5*sqrt(57))) / 19.
%F (End)
%e Some solutions for n=4:
%e ..0..1. .0..2. .0..1. .0..1. .0..1. .0..1. .0..1. .0..2. .0..2. .0..2
%e ..0..2. .1..2. .0..2. .0..2. .0..2. .2..2. .1..2. .1..1. .1..1. .1..0
%e ..2..1. .2..0. .2..0. .1..2. .1..2. .1..1. .0..1. .0..1. .0..2. .2..1
%e ..2..0. .2..1. .1..1. .0..0. .1..1. .0..2. .0..0. .2..2. .1..1. .0..1
%Y Column 2 of A278014.
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 08 2016
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