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%I #8 Nov 18 2018 09:57:32
%S 1029,2361,4239,6663,9633,13149,17211,21819,26973,32673,38919,45711,
%T 53049,60933,69363,78339,87861,97929,108543,119703,131409,143661,
%U 156459,169803,183693,198129,213111,228639,244713,261333,278499,296211,314469
%N Number of (4+1) X (n+1) 0..2 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="/A250759/b250759.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 273*n^2 + 513*n + 243.
%F Conjectures from _Colin Barker_, Nov 18 2018: (Start)
%F G.f.: 3*x*(343 - 242*x + 81*x^2) / (1 - x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F (End)
%e Some solutions for n=4:
%e ..2..2..2..2..2....2..2..2..2..2....0..0..0..0..0....1..1..1..1..1
%e ..2..2..2..2..2....0..0..0..0..0....0..0..1..1..1....0..0..1..1..1
%e ..0..0..0..1..1....0..0..0..0..0....0..0..1..1..1....1..1..2..2..2
%e ..1..1..1..2..2....2..2..2..2..2....1..1..2..2..2....0..0..1..1..1
%e ..0..1..1..2..2....1..1..1..2..2....0..0..1..2..2....0..0..1..1..2
%Y Row 4 of A250755.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 27 2014