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A197311 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.

%I A197311 #9 May 12 2018 08:45:54
%S A197311 1,0,3,2,9,6,27,18,83,56,257,176,797,556,2475,1766,7699,5640,23995,
%T A197311 18106,74937,58408,234541,189266,735771,615834,2313757,2011340,
%U A197311 7294375,6591454,23056393,21667064,73073221,71416640,232226565,235964308,740061147
%N A197311 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 0,1,1,0,0 for x=0,1,2,3,4.
%C A197311 Every 0 is next to 0 0's, every 1 is next to 1 1's, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 0's.
%C A197311 Column 2 of A197317.
%H A197311 R. H. Hardin, <a href="/A197311/b197311.txt">Table of n, a(n) for n = 1..200</a>
%F A197311 Empirical: a(n) = a(n-1) +6*a(n-2) -6*a(n-3) -9*a(n-4) +10*a(n-5) -3*a(n-7).
%F A197311 Empirical g.f.: x*(1 - x - 3*x^2 + 5*x^3 - 2*x^4 - 7*x^5 + 6*x^6) / ((1 - 3*x^2)*(1 - x - 3*x^2 + 3*x^3 - x^5)). - _Colin Barker_, May 12 2018
%e A197311 All solutions for n=4:
%e A197311 ..1..0....0..1
%e A197311 ..1..2....2..1
%e A197311 ..2..1....1..2
%e A197311 ..0..1....1..0
%Y A197311 Cf. A197317.
%K A197311 nonn
%O A197311 1,3
%A A197311 _R. H. Hardin_, Oct 13 2011