A232042 - OEIS

%I #7 Oct 02 2018 06:31:54

%S 4,15,80,446,2477,13752,76375,424115,2355221,13079032,72630752,

%T 403334385,2239803950,12438120321,69071597937,383569664377,

%U 2130046094920,11828611039210,65686859759121,364773474308192,2025666747456127

%N Number of n X 3 0..1 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.

%H R. H. Hardin, <a href="/A232042/b232042.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 9*a(n-2) -a (n-3) - 6*a(n-4) for n>5.

%F Empirical g.f.: x*(4 - x - 16*x^2 - 5*x^3 + 12*x^4) / (1 - 4*x - 9*x^2 + x^3 + 6*x^4). - _Colin Barker_, Oct 02 2018

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A232047.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 17 2013