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A250815 Number of (3+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 A250815 #8 Nov 21 2018 06:14:01
%S A250815 432,1315,3081,6171,11116,18537,29145,43741,63216,88551,120817,161175,
%T A250815 210876,271261,343761,429897,531280,649611,786681,944371,1124652,
%U A250815 1329585,1561321,1822101,2114256,2440207,2802465,3203631,3646396,4133541,4667937
%N A250815 Number of (3+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 A250815 R. H. Hardin, <a href="/A250815/b250815.txt">Table of n, a(n) for n = 1..210</a>
%F A250815 Empirical: a(n) = (15/4)*n^4 + 36*n^3 + (527/4)*n^2 + (359/2)*n + 81.
%F A250815 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250815 G.f.: x*(432 - 845*x + 826*x^2 - 404*x^3 + 81*x^4) / (1 - x)^5.
%F A250815 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 A250815 (End)
%e A250815 Some solutions for n=4:
%e A250815 ..1..2..2..2..2....2..1..1..2..2....2..2..1..0..0....1..1..1..1..1
%e A250815 ..0..1..1..1..1....1..1..1..2..2....0..0..0..0..0....1..1..1..2..2
%e A250815 ..1..2..2..2..2....1..1..1..2..2....0..0..0..0..1....1..1..1..2..2
%e A250815 ..1..2..2..2..2....1..1..1..2..2....0..0..1..1..2....0..0..0..1..1
%Y A250815 Row 3 of A250812.
%K A250815 nonn
%O A250815 1,1
%A A250815 _R. H. Hardin_, Nov 27 2014