%I #7 Nov 14 2018 09:36:36

%S 44,217,1000,4535,20242,89677,395240,1736779,7617286,33369545,

%T 146077396,639173575,2795963426,12228336613,53475556816,233837032739,

%U 1022474657182,4470747289345,19547912489996,85470468806527,373705021918234

%N Number of (n+1)X(1+1) 0..2 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

%H R. H. Hardin, <a href="/A250447/b250447.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 20*a(n-3) + 6*a(n-4) + 12*a(n-5).

%F Empirical g.f.: x*(44 - 47*x - 170*x^2 + 66*x^3 + 108*x^4) / ((1 - x)*(1 - 2*x - 2*x^2)*(1 - 3*x - 6*x^2)). - _Colin Barker_, Nov 14 2018

%e Some solutions for n=6:

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

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

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

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

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

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

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

%Y Column 1 of A250454.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 23 2014