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A196294 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.

%I A196294 #8 May 08 2018 09:58:59
%S A196294 3,9,20,61,187,536,1597,4849,14582,44097,134349,409428,1249517,
%T A196294 3822519,11705002,35866253,109991817,337493970,1035913925,3180693901,
%U A196294 9768462112,30005758115,92181317503,283222651372,870256732085,2674196289015
%N A196294 Number of n X 2 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,0,1,4,2 for x=0,1,2,3,4.
%C A196294 Every 0 is next to 0 3's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 4's, every 4 is next to 4 2's.
%C A196294 Column 2 of A196300.
%H A196294 R. H. Hardin, <a href="/A196294/b196294.txt">Table of n, a(n) for n = 1..200</a>
%F A196294 Empirical: a(n) = 2*a(n-1) +4*a(n-2) +6*a(n-3) -9*a(n-4) -38*a(n-5) -32*a(n-6) -11*a(n-7) +6*a(n-8) +a(n-9).
%F A196294 Empirical g.f.: x*(1 + x)^2*(3 - 3*x - 7*x^2 - 16*x^3 - 3*x^4 + 15*x^5 + 2*x^6) / ((1 - x - 7*x^3 - x^4)*(1 - x - 5*x^2 - 4*x^3 - x^4 + x^5)). - _Colin Barker_, May 08 2018
%e A196294 Some solutions for n=4:
%e A196294 ..0..0....1..0....1..2....1..0....0..0....2..1....0..1....1..0....0..1....1..0
%e A196294 ..2..1....1..0....0..1....1..0....0..0....1..0....0..2....2..0....0..2....2..1
%e A196294 ..1..1....1..1....0..1....1..0....0..0....1..1....2..1....1..0....0..1....2..1
%e A196294 ..0..0....0..1....1..2....2..1....1..1....0..1....1..0....1..0....1..2....1..0
%Y A196294 Cf. A196300.
%K A196294 nonn
%O A196294 1,1
%A A196294 _R. H. Hardin_, Sep 30 2011