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%I
%S 1,3,16,37,120,420,1468,4801,15885,53128,178165,594582,1983454,
%T 6622194,22119691,73864009,246623786,823483995,2749775102,9181948002,
%U 30659615818,102376096183,341847401583,1141474348346,3811532000911,12727199593820
%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.
%C Every 0 is next to 0 4'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 1's.
%C Column 3 of A196809.
%H R. H. Hardin, <a href="/A196804/b196804.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n-1) +2*a(n-2) +3*a(n-3) +17*a(n-4) +3*a(n-5) -4*a(n-6).
%F Empirical g.f.: x*(1 + x + 8*x^2 - 4*x^3 - 12*x^4 + 4*x^5) / (1 - 2*x - 2*x^2 - 3*x^3 - 17*x^4 - 3*x^5 + 4*x^6). - _Colin Barker_, May 09 2018
%e Some solutions for n=4:
%e ..0..0..0....0..3..0....0..0..0....0..3..0....0..3..0....0..3..0....0..0..0
%e ..0..0..3....0..0..0....0..0..0....0..0..0....0..0..3....3..0..3....3..0..3
%e ..3..0..0....3..0..0....3..0..3....0..0..3....0..0..0....0..0..0....0..0..0
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..3..0....0..0..0....0..3..0
%Y Cf. A196809.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 06 2011
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