%I
%S 1,3,16,37,117,372,1168,3613,11247,35047,109150,339828,1058164,
%T 3295056,10260427,31949551,99486794,309789423,964645058,3003782043,
%U 9353396014,29125288852,90692454357,282404795252,879372700786,2738255017364
%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,2,3,0,4 for x=0,1,2,3,4.
%C Every 0 is next to 0 1's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 4's.
%C Column 3 of A196578.
%H R. H. Hardin, <a href="/A196573/b196573.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n1) +2*a(n2) +3*a(n3) +5*a(n4) a(n6).
%F Empirical g.f.: x*(1 + x + 8*x^2  4*x^3  3*x^4 + x^5) / ((1 + x)*(1  3*x + x^2  4*x^3  x^4 + x^5)).  _Colin Barker_, May 09 2018
%e Some solutions for n=4:
%e ..0..3..0....0..3..0....0..0..0....0..0..0....0..3..0....0..0..0....0..0..0
%e ..3..0..0....0..0..3....0..3..0....3..0..0....0..0..0....0..0..3....0..0..0
%e ..0..0..0....0..0..0....0..3..0....0..0..3....0..0..0....0..0..0....3..0..0
%e ..0..0..0....0..3..0....0..0..0....0..3..0....0..3..0....0..0..0....0..3..0
%Y Cf. A196578.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 04 2011
