A250762 Number of (7+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.

29012, 67356, 121593, 191723, 277746, 379662, 497471, 631173, 780768, 946256, 1127637, 1324911, 1538078, 1767138, 2012091, 2272937, 2549676, 2842308, 3150833, 3475251, 3815562, 4171766, 4543863, 4931853, 5335736, 5755512, 6191181, 6642743

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..134

Formula

Empirical: a(n) = (15893/2)*n^2 + (29009/2)*n + 6561.

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

G.f.: x*(29012 - 19680*x + 6561*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:
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....1..1..1..1..1
..2..2..2..2..2....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..2..2..2..2..2....0..0..0..0..0....0..0..0..0..0....1..1..1..1..1
..0..0..0..0..0....1..1..1..1..1....2..2..2..2..2....1..1..1..1..1
..0..0..0..0..0....2..2..2..2..2....2..2..2..2..2....1..1..1..1..1
..2..2..2..2..2....1..1..1..1..1....0..0..0..0..0....2..2..2..2..2
..2..2..2..2..2....0..0..0..0..1....1..1..1..1..1....0..0..0..0..0
..1..1..2..2..2....0..0..0..0..1....0..0..1..2..2....1..2..2..2..2

Crossrefs

Row 7 of A250755.

Sequence in context: A235817 A235576 A206017 * A249465 A257391 A015313

Adjacent sequences: A250759 A250760 A250761 * A250763 A250764 A250765

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved