A196631 - OEIS

%I #8 Mar 01 2018 09:42:51

%S 1,5,21,62,232,780,2716,9427,32612,113008,391387,1355818,4696609,

%T 16268643,56353996,195208062,676193929,2342310759,8113674993,

%U 28105465903,97356282867,337238520190,1168181597226,4046537274472,14017053521933

%N Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,3,2,0,4 for x=0,1,2,3,4.

%C Every 0 is next to 0 1's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 0's, every 4 is next to 4 4's.

%C Column 3 of A196636.

%H R. H. Hardin, <a href="/A196631/b196631.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) + 4*a(n-3) + 5*a(n-4) + 5*a(n-5) - 12*a(n-6) - a(n-8) - 4*a(n-9) for n>10.

%F Empirical g.f.: x*(1 + 2*x + 6*x^2 - 5*x^3 + 21*x^4 - 30*x^5 + 10*x^6 - 4*x^7 - 6*x^8 + x^9) / (1 - 3*x - 4*x^3 - 5*x^4 - 5*x^5 + 12*x^6 + x^8 + 4*x^9). - _Colin Barker_, Mar 01 2018

%e Some solutions for n=4:

%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..3..0....0..3..0....0..0..0

%e ..0..0..3....0..2..2....0..0..3....3..0..0....0..0..0....0..0..3....0..0..0

%e ..0..0..0....0..2..2....3..0..0....0..2..2....0..0..3....3..0..0....3..0..3

%e ..0..3..0....0..0..0....0..0..0....0..2..2....0..3..0....0..0..0....0..0..0

%Y Cf. A196636.

%K nonn

%O 1,2

%A _R. H. Hardin_, Oct 04 2011