A250760 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 x(i,j)+x(i-1,j) in the j direction.

3152, 7272, 13089, 20603, 29814, 40722, 53327, 67629, 83628, 101324, 120717, 141807, 164594, 189078, 215259, 243137, 272712, 303984, 336953, 371619, 407982, 446042, 485799, 527253, 570404, 615252, 661797, 710039, 759978, 811614, 864947

Offset

1,1

Links

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

Formula

Empirical: a(n) = (1697/2)*n^2 + (3149/2)*n + 729.

Conjectures from Colin Barker, Nov 18 2018: (Start)

G.f.: x*(3152 - 2184*x + 729*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..1....0..0..0..0..0....1..1..1..1..1....0..0..0..0..0
..2..2..2..2..2....1..1..1..1..1....0..0..0..0..1....2..2..2..2..2
..2..2..2..2..2....2..2..2..2..2....1..1..1..1..2....2..2..2..2..2
..2..2..2..2..2....1..1..1..1..1....0..0..0..0..1....1..1..1..1..1
..1..2..2..2..2....1..1..1..1..1....1..1..1..1..2....0..0..1..1..1
..0..2..2..2..2....0..0..0..0..0....0..0..1..1..2....0..0..2..2..2

Crossrefs

Row 5 of A250755.

Sequence in context: A172720 A276686 A252215 * A184452 A151750 A031610

Adjacent sequences: A250757 A250758 A250759 * A250761 A250762 A250763

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved