%I #7 Nov 22 2018 08:23:32

%S 90,440,2002,8736,37130,155080,640002,2619056,10653370,43144920,

%T 174174002,701478976,2820264810,11324105960,45425564002,182089676496,

%U 729520967450,2921570654200,11696742970002,46818352939616

%N Number of (n+1) X (1+1) 0..3 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="/A250870/b250870.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3); a(n) = (128*4^n - 81*3^n + 1)/3.

%F Empirical g.f.: 2*x*(45 - 140*x + 96*x^2) / ((1 - x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 22 2018

%e Some solutions for n=4:

%e ..1..1....0..1....2..2....2..3....0..1....2..1....2..2....1..2....2..2....0..0

%e ..0..0....2..3....0..0....1..2....1..2....1..2....1..1....0..1....1..1....1..1

%e ..0..0....0..1....1..1....0..2....0..2....2..3....1..1....2..3....1..1....2..2

%e ..2..3....0..1....3..3....0..3....0..2....1..3....0..1....0..1....2..3....0..0

%e ..0..1....1..3....0..1....0..3....0..3....0..2....0..1....0..3....2..3....1..1

%Y Column 1 of A250877.

%K nonn

%O 1,1

%A _R. H. Hardin_, Nov 28 2014