A196573 - OEIS

%I #8 May 09 2018 08:16:59

%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(n-1) +2*a(n-2) +3*a(n-3) +5*a(n-4) -a(n-6).

%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