%I
%S 1,5,14,44,149,479,1537,4971,16088,52020,168111,543379,1756623,
%T 5678611,18356490,59338576,191817551,620069245,2004431603,6479507953,
%U 20945607368,67708621756,218874399841,707531760601,2287161925185,7393462782885
%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,2,1,0 for x=0,1,2,3,4.
%C Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 0's.
%C Column 3 of A197217.
%H R. H. Hardin, <a href="/A197212/b197212.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 2*a(n1) +8*a(n3) +10*a(n4) +16*a(n5) +8*a(n6) +6*a(n7) 8*a(n8) 12*a(n9) 10*a(n10) 4*a(n11) a(n12).
%F Empirical g.f.: x*(1 + 3*x + 4*x^2 + 8*x^3 + 11*x^4 + 3*x^5  x^6  5*x^7  14*x^8  10*x^9  5*x^10  x^11) / (1  2*x  8*x^3  10*x^4  16*x^5  8*x^6  6*x^7 + 8*x^8 + 12*x^9 + 10*x^10 + 4*x^11 + x^12).  _Colin Barker_, May 11 2018
%e Some solutions for n=4:
%e ..0..1..0....0..0..0....0..0..0....1..3..1....0..0..0....2..2..0....2..2..0
%e ..1..3..1....2..2..2....0..0..0....0..1..0....1..0..0....2..2..0....2..2..0
%e ..2..2..0....2..0..2....0..2..2....0..0..0....3..1..0....0..0..0....0..1..0
%e ..2..2..0....2..2..2....0..2..2....0..0..0....1..0..0....0..0..0....1..3..1
%Y Cf. A197217.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 11 2011
