%I #8 Nov 22 2018 11:34:01
%S 440,1456,3442,6728,11644,18520,27686,39472,54208,72224,93850,119416,
%T 149252,183688,223054,267680,317896,374032,436418,505384,581260,
%U 664376,755062,853648,960464,1075840,1200106,1333592,1476628,1629544,1792670
%N Number of (2+1) X (n+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="/A250879/b250879.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 55*n^3 + 155*n^2 + 166*n + 64.
%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F G.f.: 2*x*(220 - 152*x + 129*x^2 - 32*x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=4:
%e ..1..1..1..1..1....2..2..2..2..0....3..3..3..3..3....2..2..2..2..2
%e ..2..2..2..2..3....1..1..1..1..3....1..1..1..2..2....2..2..3..3..3
%e ..1..1..1..1..3....0..0..0..1..3....0..1..1..2..3....0..1..3..3..3
%Y Row 2 of A250877.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014