A202973 - OEIS

%I #8 Feb 19 2018 08:25:57

%S 1,2,4,7,14,31,69,155,354,814,1875,4326,9993,23095,53387,123430,

%T 285394,659913,1525942,3528541,8159347,18867623,43629460,100888804,

%U 233295503,539473228,1247479743,2884676711,6670537293,15424975984,35668774074

%N Number of n X 2 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.

%C Column 2 of A202979.

%H R. H. Hardin, <a href="/A202973/b202973.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).

%F Empirical g.f.: x*(1 - x - 3*x^3 - x^4) / (1 - 3*x + 2*x^2 - 2*x^3 + 2*x^4 + x^5). - _Colin Barker_, Feb 19 2018

%e Some solutions for n=5:

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

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

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

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

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

%K nonn

%O 1,2

%A _R. H. Hardin_, Dec 26 2011