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%I #8 Nov 22 2018 11:34:08
%S 90,288,678,1328,2306,3680,5518,7888,10858,14496,18870,24048,30098,
%T 37088,45086,54160,64378,75808,88518,102576,118050,135008,153518,
%U 173648,195466,219040,244438,271728,300978,332256,365630,401168,438938,479008,521446
%N Number of (1+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="/A250878/b250878.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (34/3)*n^3 + 28*n^2 + (104/3)*n + 16.
%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F G.f.: 2*x*(45 - 36*x + 33*x^2 - 8*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 ..3..3..2..3..3....2..1..1..1..1....2..2..3..3..3....2..2..2..1..0
%e ..0..0..1..2..2....0..1..1..1..3....1..1..2..2..3....1..1..1..2..3
%Y Row 1 of A250877.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014
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