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A250524 Number of (n+1)X(5+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 A250524 #7 Nov 14 2018 14:05:43
%S A250524 10660,65310,279161,993123,3183434,9580060,27710543,78195145,
%T A250524 217483704,600720730,1657359573,4587075263,12774934710,35868804392,
%U A250524 101626338475,290581221893,838071567940,2435917896966,7127659997521,20972608975899
%N A250524 Number of (n+1)X(5+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 A250524 R. H. Hardin, <a href="/A250524/b250524.txt">Table of n, a(n) for n = 1..210</a>
%F A250524 Empirical: a(n) = 14*a(n-1) - 85*a(n-2) + 294*a(n-3) - 639*a(n-4) + 906*a(n-5) - 839*a(n-6) + 490*a(n-7) - 164*a(n-8) + 24*a(n-9).
%F A250524 Empirical g.f.: x*(10660 - 83930*x + 270921*x^2 - 497821*x^3 + 618997*x^4 - 570765*x^5 + 360190*x^6 - 119532*x^7 + 17496*x^8) / ((1 - x)^5*(1 - 2*x)^3*(1 - 3*x)). - _Colin Barker_, Nov 14 2018
%e A250524 Some solutions for n=2:
%e A250524 ..0..1..0..0..0..1....2..2..2..2..1..2....2..1..1..0..1..0....1..1..2..0..1..0
%e A250524 ..1..2..1..1..1..2....1..1..1..1..1..2....1..1..1..0..1..0....1..1..2..0..1..0
%e A250524 ..0..1..1..1..1..2....0..0..0..0..1..2....1..2..2..1..2..1....0..1..2..0..1..1
%Y A250524 Column 5 of A250527.
%K A250524 nonn
%O A250524 1,1
%A A250524 _R. H. Hardin_, Nov 24 2014