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%I #9 Nov 22 2018 08:23:45
%S 288,1456,6812,30360,131068,553736,2304492,9488920,38773148,157554216,
%T 637620172,2572727480,10357724028,41631485896,167128007852,
%U 670318814040,2686696783708,10763054076776,43101021851532,172550513476600
%N Number of (n+1) X (2+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="/A250871/b250871.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (472*4^n - 378*3^n + 54*2^n + 2)/3.
%F Empirical g.f.: 4*x*(72 - 356*x + 583*x^2 - 300*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - _Colin Barker_, Nov 22 2018
%e Some solutions for n=4:
%e ..3..3..3....1..1..1....0..0..0....0..1..1....3..3..3....2..2..2....1..1..1
%e ..1..1..1....2..2..2....0..1..1....0..1..1....1..1..2....0..0..0....1..1..1
%e ..3..3..3....2..2..2....1..2..2....1..2..2....0..0..2....2..3..3....2..3..3
%e ..1..1..1....1..1..3....0..1..2....1..2..2....1..1..3....1..2..2....0..1..1
%e ..0..0..3....0..1..3....0..2..3....1..2..2....1..1..3....0..1..3....0..1..3
%Y Column 2 of A250877.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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