A231376 - OEIS

%I #8 Mar 18 2018 06:59:19

%S 2,10,21,48,113,261,601,1390,3216,7435,17190,39751,91921,212555,

%T 491510,1136570,2628207,6077470,14053561,32497507,75147355,173771026,

%U 401828790,929190453,2148663614,4968578109,11489359399,26568039511,61436038272

%N Number of n X 2 0..1 arrays with no element less than a strict majority of its horizontal and vertical neighbors.

%C Column 2 of A231382.

%H R. H. Hardin, <a href="/A231376/b231376.txt">Table of n, a(n) for n = 1..210</a>

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

%F Empirical g.f.: x*(2 + 4*x - 5*x^2 + x^3 - 5*x^4 - 2*x^5) / (1 - 3*x + 2*x^2 - 2*x^3 + 2*x^4 + x^5). - _Colin Barker_, Mar 18 2018

%e Some solutions for n=3:

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

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

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

%Y Cf. A231382.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 08 2013