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A250760 Number of (5+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.

%I A250760 #8 Nov 18 2018 09:01:03
%S A250760 3152,7272,13089,20603,29814,40722,53327,67629,83628,101324,120717,
%T A250760 141807,164594,189078,215259,243137,272712,303984,336953,371619,
%U A250760 407982,446042,485799,527253,570404,615252,661797,710039,759978,811614,864947
%N A250760 Number of (5+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 A250760 R. H. Hardin, <a href="/A250760/b250760.txt">Table of n, a(n) for n = 1..210</a>
%F A250760 Empirical: a(n) = (1697/2)*n^2 + (3149/2)*n + 729.
%F A250760 Conjectures from _Colin Barker_, Nov 18 2018: (Start)
%F A250760 G.f.: x*(3152 - 2184*x + 729*x^2) / (1 - x)^3.
%F A250760 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250760 (End)
%e A250760 Some solutions for n=4:
%e A250760 ..1..1..1..1..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
%e A250760 ..2..2..2..2..2....1..1..1..1..1....0..0..0..0..1....2..2..2..2..2
%e A250760 ..2..2..2..2..2....2..2..2..2..2....1..1..1..1..2....2..2..2..2..2
%e A250760 ..2..2..2..2..2....1..1..1..1..1....0..0..0..0..1....1..1..1..1..1
%e A250760 ..1..2..2..2..2....1..1..1..1..1....1..1..1..1..2....0..0..1..1..1
%e A250760 ..0..2..2..2..2....0..0..0..0..0....0..0..1..1..2....0..0..2..2..2
%Y A250760 Row 5 of A250755.
%K A250760 nonn
%O A250760 1,1
%A A250760 _R. H. Hardin_, Nov 27 2014