A195964 - OEIS

%I #9 May 08 2018 06:20:08

%S 2,2,5,7,14,25,35,56,107,173,284,491,805,1338,2299,3817,6348,10741,

%T 17955,29996,50517,84551,141438,237601,398131,666648,1118507,1874589,

%U 3140516,5266459,8827461,14792378,24799555,41569097,69668012,116786117,195757315

%N Number of n X 3 0..4 arrays with each element equal to the number its horizontal and vertical neighbors equal to itself.

%C Column 3 of A195969.

%H R. H. Hardin, <a href="/A195964/b195964.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 2*a(n-3) +2*a(n-4) +2*a(n-5) +4*a(n-6) -a(n-9) for n>11.

%F Empirical g.f.: x*(2 + 2*x + 5*x^2 + 3*x^3 + 6*x^4 + 7*x^5 - x^6 - 4*x^7 - 5*x^8 - x^9 - 2*x^10) / (1 - 2*x^3 - 2*x^4 - 2*x^5 - 4*x^6 + x^9). - _Colin Barker_, May 08 2018

%e All solutions for n=4:

%e ..0..1..1....2..2..2....2..2..2....0..1..1....1..1..0....2..2..2....1..1..0

%e ..1..2..2....2..0..2....2..0..2....2..2..2....2..2..1....2..1..2....2..2..2

%e ..1..2..2....2..2..2....2..2..2....2..0..2....2..2..1....2..1..2....2..0..2

%e ..0..1..1....1..1..0....0..1..1....2..2..2....1..1..0....2..2..2....2..2..2

%Y Cf. A195969.

%K nonn

%O 1,1

%A _R. H. Hardin_, Sep 25 2011