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%I #6 Jul 04 2012 07:46:20
%S 9,4,121,180,2041,5068,37441,121588,722009,2720828,14363985,58850116,
%T 291217929,1250645324,5970338241,26327622356,123189300217,
%U 551369047260,2551171130801,11514142774628,52942859314409,240066004887660
%N Number of 0..2 colorings of a 3X(n+1) array circular in the n+1 direction with new values 0..2 introduced in row major order
%C Row 3 of A214101
%H R. H. Hardin, <a href="/A214102/b214102.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +15*a(n-2) -33*a(n-3) -22*a(n-4) +38*a(n-5) +8*a(n-6) -8*a(n-7).
%F Empirical: G.f. -x*(2*x^2-1)*(8*x^3-8*x^2-23*x+9) / ( (x-1)*(2*x-1)*(1+x)*(2*x^2-5*x+1)*(2*x^2+4*x+1) ). - _R. J. Mathar_, Jul 04 2012
%e Some solutions for n=4
%e ..0..1..0..2..1....0..1..0..1..2....0..1..2..0..1....0..1..2..0..1
%e ..1..2..1..0..2....2..0..2..0..1....2..0..1..2..0....1..2..1..2..0
%e ..0..1..0..2..1....0..1..0..1..2....0..1..2..1..2....2..0..2..0..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Jul 04 2012