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A250854 Number of (2+1) X (n+1) 0..3 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 A250854 #8 Nov 21 2018 11:26:42
%S A250854 543,2457,8037,21436,49599,103293,198297,356752,608671,993609,1562493,
%T A250854 2379612,3524767,5095581,7209969,10008768,13658527,18354457,24323541,
%U A250854 31827804,41167743,52685917,66770697,83860176,104446239,129078793
%N A250854 Number of (2+1) X (n+1) 0..3 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 A250854 R. H. Hardin, <a href="/A250854/b250854.txt">Table of n, a(n) for n = 1..210</a>
%F A250854 Empirical: a(n) = (2/9)*n^6 + (47/12)*n^5 + (953/36)*n^4 + (1141/12)*n^3 + (6527/36)*n^2 + 172*n + 64.
%F A250854 Conjectures from _Colin Barker_, Nov 21 2018: (Start)
%F A250854 G.f.: x*(543 - 1344*x + 2241*x^2 - 2231*x^3 + 1334*x^4 - 447*x^5 + 64*x^6) / (1 - x)^7.
%F A250854 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A250854 (End)
%e A250854 Some solutions for n=4:
%e A250854 ..2..2..1..1..1....2..1..0..0..0....3..3..3..1..2....3..2..3..1..1
%e A250854 ..1..1..1..1..1....0..0..1..1..2....0..0..0..0..1....0..0..1..1..1
%e A250854 ..2..3..3..3..3....0..0..1..2..3....1..2..2..2..3....0..0..2..2..2
%Y A250854 Row 2 of A250853.
%K A250854 nonn
%O A250854 1,1
%A A250854 _R. H. Hardin_, Nov 28 2014