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.

32, 72, 129, 203, 294, 402, 527, 669, 828, 1004, 1197, 1407, 1634, 1878, 2139, 2417, 2712, 3024, 3353, 3699, 4062, 4442, 4839, 5253, 5684, 6132, 6597, 7079, 7578, 8094, 8627, 9177, 9744, 10328, 10929, 11547, 12182, 12834, 13503, 14189, 14892, 15612

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (17/2)*n^2 + (29/2)*n + 9.

Conjectures from Colin Barker, Nov 17 2018: (Start)

G.f.: x*(32 - 24*x + 9*x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)

Example

Some solutions for n=4:
..1..1..1..1..0....0..0..0..1..0....0..0..0..1..1....2..2..1..1..0
..1..1..1..1..2....0..0..0..1..2....1..1..1..2..2....0..0..1..1..2

Crossrefs

Row 1 of A250755.

Sequence in context: A104026 A216417 A110230 * A303583 A224220 A007797

Adjacent sequences: A250753 A250754 A250755 * A250757 A250758 A250759

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved