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%I #7 Oct 07 2018 14:34:56
%S 3,11,65,386,2315,13886,83315,499886,2999315,17995886,107975315,
%T 647851886,3887111315,23322667886,139936007315,839616043886,
%U 5037696263315,30226177579886,181357065479315,1088142392875886
%N Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
%H R. H. Hardin, <a href="/A233099/b233099.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) + a(n-2) - 6*a(n-3) for n>4.
%F Conjectures from _Colin Barker_, Oct 07 2018: (Start)
%F G.f.: x*(3 - 7*x - 4*x^2 + 3*x^3) / ((1 - x)*(1 + x)*(1 - 6*x)).
%F a(n) = (24 + 25*6^n) / 84 for n even.
%F a(n) = (60 + 25*6^n) / 84 for n>1 and odd.
%F (End)
%e Some solutions for n=5:
%e ..0..1..0..1..3....0..1..3..2..0....0..0..0..0..1....0..1..1..1..0
%e ..0..0..1..1..3....0..2..0..1..0....1..0..1..0..1....0..0..1..0..1
%Y Row 2 of A233098.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 04 2013