A250761 Number of (6+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.

9585, 22197, 40023, 63063, 91317, 124785, 163467, 207363, 256473, 310797, 370335, 435087, 505053, 580233, 660627, 746235, 837057, 933093, 1034343, 1140807, 1252485, 1369377, 1491483, 1618803, 1751337, 1889085, 2032047, 2180223, 2333613

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..209

Formula

Empirical: a(n) = 2607*n^2 + 4791*n + 2187.

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

G.f.: 3*x*(3195 - 2186*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:
..2..2..2..2..2....0..0..0..0..0....2..2..2..2..2....2..2..2..2..2
..0..0..0..0..0....1..1..1..1..1....1..1..1..1..1....0..0..0..0..0
..2..2..2..2..2....1..1..1..2..2....0..0..0..0..0....2..2..2..2..2
..2..2..2..2..2....0..0..0..1..1....1..1..1..1..1....2..2..2..2..2
..2..2..2..2..2....0..0..0..1..1....2..2..2..2..2....2..2..2..2..2
..1..2..2..2..2....1..1..1..2..2....0..1..1..1..1....1..1..1..1..1
..0..1..1..2..2....1..1..1..2..2....0..2..2..2..2....0..0..0..0..2

Crossrefs

Row 6 of A250755.

Sequence in context: A133449 A275687 A210409 * A038825 A038814 A230020

Adjacent sequences: A250758 A250759 A250760 * A250762 A250763 A250764

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved