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A250817 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 min(x(i,j),x(i-1,j)) in the j direction.

%I A250817 #7 Nov 21 2018 06:14:20
%S A250817 4356,13735,32745,66291,120304,201741,318585,479845,695556,976779,
%T A250817 1335601,1785135,2339520,3013921,3824529,4788561,5924260,7250895,
%U A250817 8788761,10559179,12584496,14888085,17494345,20428701,23717604,27388531,31469985
%N A250817 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 min(x(i,j),x(i-1,j)) in the j direction.
%H A250817 R. H. Hardin, <a href="/A250817/b250817.txt">Table of n, a(n) for n = 1..210</a>
%F A250817 Empirical: a(n) = (171/4)*n^4 + 390*n^3 + (5627/4)*n^2 + (3575/2)*n + 729.
%F A250817 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250817 G.f.: x*(4356 - 8045*x + 7630*x^2 - 3644*x^3 + 729*x^4) / (1 - x)^5.
%F A250817 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A250817 (End)
%e A250817 Some solutions for n=4:
%e A250817 ..1..1..1..2..2....0..0..0..0..0....2..2..2..0..1....2..0..0..0..0
%e A250817 ..1..1..1..2..2....1..1..1..1..1....0..0..0..0..1....0..0..0..0..0
%e A250817 ..1..1..1..2..2....1..1..1..1..1....0..0..0..0..1....1..1..1..1..1
%e A250817 ..0..0..0..1..1....0..0..0..0..0....1..1..1..1..2....0..0..0..0..0
%e A250817 ..0..0..1..2..2....0..0..2..2..2....1..1..1..1..2....0..0..0..0..0
%e A250817 ..0..0..1..2..2....0..0..2..2..2....0..0..0..0..1....0..1..1..1..2
%Y A250817 Row 5 of A250812.
%K A250817 nonn
%O A250817 1,1
%A A250817 _R. H. Hardin_, Nov 27 2014