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A233083 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

%I A233083 #8 Oct 07 2018 08:21:23
%S A233083 3,14,95,662,4631,32414,226895,1588262,11117831,77824814,544773695,
%T A233083 3813415862,26693911031,186857377214,1308001640495,9156011483462,
%U A233083 64092080384231,448644562689614,3140511938827295,21983583571791062
%N A233083 Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
%H A233083 R. H. Hardin, <a href="/A233083/b233083.txt">Table of n, a(n) for n = 1..210</a>
%F A233083 Empirical: a(n) = 8*a(n-1) - 7*a(n-2) for n>3.
%F A233083 Conjectures from _Colin Barker_, Oct 07 2018: (Start)
%F A233083 G.f.: x*(3 - 10*x + 4*x^2) / ((1 - x)*(1 - 7*x)).
%F A233083 a(n) = (49 + 27*7^n) / 98 for n>1.
%F A233083 (End)
%e A233083 Some solutions for n=5:
%e A233083 ..0..1..1..3..2....0..0..1..0..2....0..1..1..3..3....0..1..0..2..0
%e A233083 ..1..3..2..2..3....2..0..1..0..0....1..1..3..3..3....0..1..0..0..0
%Y A233083 Row 2 of A233082.
%K A233083 nonn
%O A233083 1,1
%A A233083 _R. H. Hardin_, Dec 03 2013