%I #9 May 09 2018 15:56:20
%S 1,4,12,35,102,281,787,2237,6346,17976,50903,144132,408157,1155913,
%T 3273609,9270960,26255482,74355847,210576950,596357727,1688896077,
%U 4782984549,13545499068,38361099308,108639331309,307668565890
%N Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 3,4,2,0,1 for x=0,1,2,3,4.
%C Every 0 is next to 0 3's, every 1 is next to 1 4's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 1's.
%C Column 4 of A196863.
%H R. H. Hardin, <a href="/A196859/b196859.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) +a(n-5) -3*a(n-6) -6*a(n-7) -8*a(n-8) -8*a(n-9) -3*a(n-10).
%F Empirical g.f.: x*(1 + x + x^2 + x^3 + 2*x^4 - 11*x^5 - 13*x^6 - 6*x^7 - 5*x^8 - 3*x^9) / (1 - 3*x + x^2 - 2*x^3 + x^4 - x^5 + 3*x^6 + 6*x^7 + 8*x^8 + 8*x^9 + 3*x^10). - _Colin Barker_, May 09 2018
%e Some solutions for n=5:
%e ..0..2..2..0....0..2..2..2....0..0..0..0....0..0..0..0....2..2..0..0
%e ..0..2..2..0....2..2..0..2....0..0..0..0....2..2..0..0....2..2..0..0
%e ..0..0..0..0....2..0..0..2....0..0..0..0....2..2..0..0....0..1..0..0
%e ..0..2..2..0....2..2..2..2....0..0..0..0....0..0..2..2....1..4..1..0
%e ..0..2..2..0....0..0..0..0....0..0..0..0....0..0..2..2....0..1..0..0
%Y Cf. A196863.
%K nonn
%O 1,2
%A _R. H. Hardin_, Oct 06 2011
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