A250610 Number of (n+1) X (7+1) 0..1 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.

1013, 2336, 4353, 7320, 11749, 18664, 30113, 50192, 87093, 157200, 293281, 560872, 1091045, 2145944, 4249857, 8451360, 16847605, 33632896, 67195841, 134313656, 268540773, 536986056, 1073867233, 2147619760, 4295114549, 8590093424

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).

Conjectures from Colin Barker, Nov 15 2018: (Start)

G.f.: x*(1013 - 2729*x + 1790*x^2 - 512*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 15 2018

a(n) = 128 + 2^(7+n) + 410*n + 219*n^2.

(End)

Example

Some solutions for n=6:
..1..0..1..1..1..1..0..0....1..1..1..1..1..1..1..0....1..1..1..1..0..1..0..0
..1..0..1..1..1..1..0..0....1..1..1..1..1..1..1..1....1..1..1..1..0..1..0..0
..1..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0
..1..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0
..0..0..1..1..1..1..0..1....1..1..1..1..1..1..1..1....1..1..1..1..0..1..0..0
..0..0..1..1..1..1..0..1....0..0..0..0..0..0..0..0....1..1..1..1..0..1..0..0
..0..0..1..1..1..1..0..1....1..1..1..1..1..1..1..1....1..1..1..1..0..1..1..1

Crossrefs

Column 7 of A250611.

Sequence in context: A157008 A161404 A252634 * A126239 A120214 A251267

Adjacent sequences: A250607 A250608 A250609 * A250611 A250612 A250613

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved