%I #7 Nov 15 2018 08:38:48

%S 502,1172,2236,3890,6526,10928,18664,32870,59818,112052,214660,417818,

%T 821878,1627544,3236224,6450734,12876706,25725404,51419356,102803618,

%U 205568302,411093632,822140056,1644228470,3288400666,6576740228

%N Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.

%H R. H. Hardin, <a href="/A250609/b250609.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).

%F Empirical: a(n) = 196*2^(n-1) + 99*n^2 + 177*n + 30.

%F Empirical g.f.: 2*x*(251 - 669*x + 447*x^2 - 128*x^3) / ((1 - x)^3*(1 - 2*x)). - _Colin Barker_, Nov 15 2018

%e Some solutions for n=6:

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

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

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

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

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

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

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

%Y Column 6 of A250611.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 26 2014