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%I #7 Nov 22 2018 11:33:55
%S 2002,6812,16262,31928,55386,88212,131982,188272,258658,344716,448022,
%T 570152,712682,877188,1065246,1278432,1518322,1786492,2084518,2413976,
%U 2776442,3173492,3606702,4077648,4587906,5139052,5732662,6370312,7053578
%N Number of (3+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="/A250880/b250880.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (788/3)*n^3 + 744*n^2 + (2218/3)*n + 256.
%F Conjectures from _Colin Barker_, Nov 22 2018: (Start)
%F G.f.: 2*x*(1001 - 598*x + 513*x^2 - 128*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 ..2..3..3..3..3....3..3..3..2..2....3..3..3..3..3....0..0..0..0..0
%e ..1..2..2..2..2....2..2..2..3..3....2..2..2..2..2....2..2..2..3..3
%e ..0..2..2..2..2....1..1..1..3..3....1..1..1..1..2....1..1..1..3..3
%e ..0..3..3..3..3....0..0..0..2..3....0..2..2..2..3....0..0..0..2..2
%Y Row 3 of A250877.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 28 2014