%I #5 Mar 31 2012 12:36:28
%S 2,20,120,698,4080,24074,141856,833758,4909544,28899922,170120402,
%T 1001361542,5894102732,34694985108,204224876622,1202124327402,
%U 7076038423114,41651567268298,245173129915012,1443158678807678
%N Number of nX3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,0,1,3 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 0's, every 3 is next to 3 1's, every 4 is next to 4 3's
%C Column 3 of A197047
%H R. H. Hardin, <a href="/A197042/b197042.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) +6*a(n-2) +39*a(n-3) +104*a(n-4) +320*a(n-5) -266*a(n-6) +209*a(n-7) -606*a(n-8) +472*a(n-9) -2199*a(n-10) -4220*a(n-11) -79*a(n-12) -4287*a(n-13) -1432*a(n-14) +665*a(n-15) -2303*a(n-16) -1803*a(n-17) +149*a(n-18) +1299*a(n-19) +3913*a(n-20) +1651*a(n-21) -2432*a(n-22) -901*a(n-23) +874*a(n-24) +148*a(n-25) -184*a(n-26) -32*a(n-27)
%e Some solutions for n=4
%e ..1..2..0....1..0..2....0..2..0....0..0..0....0..0..2....1..0..1....2..0..0
%e ..0..0..0....2..0..0....2..2..0....2..1..1....2..1..0....2..0..2....0..2..1
%e ..2..2..1....0..1..2....0..0..2....0..0..2....0..1..0....0..1..0....0..2..1
%e ..0..0..0....2..0..0....2..0..1....1..2..0....0..2..0....0..2..0....2..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Oct 08 2011