cp's OEIS Frontend

A250756 Number of (1+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 A250756 #8 Nov 17 2018 20:52:53
%S A250756 32,72,129,203,294,402,527,669,828,1004,1197,1407,1634,1878,2139,2417,
%T A250756 2712,3024,3353,3699,4062,4442,4839,5253,5684,6132,6597,7079,7578,
%U A250756 8094,8627,9177,9744,10328,10929,11547,12182,12834,13503,14189,14892,15612
%N A250756 Number of (1+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 A250756 R. H. Hardin, <a href="/A250756/b250756.txt">Table of n, a(n) for n = 1..210</a>
%F A250756 Empirical: a(n) = (17/2)*n^2 + (29/2)*n + 9.
%F A250756 Conjectures from _Colin Barker_, Nov 17 2018: (Start)
%F A250756 G.f.: x*(32 - 24*x + 9*x^2) / (1 - x)^3.
%F A250756 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.
%F A250756 (End)
%e A250756 Some solutions for n=4:
%e A250756 ..1..1..1..1..0....0..0..0..1..0....0..0..0..1..1....2..2..1..1..0
%e A250756 ..1..1..1..1..2....0..0..0..1..2....1..1..1..2..2....0..0..1..1..2
%Y A250756 Row 1 of A250755.
%K A250756 nonn
%O A250756 1,1
%A A250756 _R. H. Hardin_, Nov 27 2014