A250661 Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.

639, 1150, 1789, 2556, 3451, 4474, 5625, 6904, 8311, 9846, 11509, 13300, 15219, 17266, 19441, 21744, 24175, 26734, 29421, 32236, 35179, 38250, 41449, 44776, 48231, 51814, 55525, 59364, 63331, 67426, 71649, 76000, 80479, 85086, 89821, 94684, 99675

Offset

1,1

Links

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

Formula

Empirical: a(n) = 64*n^2 + 319*n + 256.

Conjectures from Colin Barker, Nov 16 2018: (Start)

G.f.: x*(639 - 767*x + 256*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....1..1..0..0..0....1..1..0..0..0....0..0..0..0..0
..0..0..0..0..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....0..0..0..0..0....1..1..1..1..1
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..0..0..0..1
..0..0..0..0..0....1..1..1..1..1....0..0..0..0..0....0..0..0..0..1
..0..0..0..0..0....0..0..1..1..1....1..1..1..1..1....0..0..0..0..1

Crossrefs

Row 7 of A250656.

Sequence in context: A360183 A281884 A200710 * A250587 A293922 A027885

Adjacent sequences: A250658 A250659 A250660 * A250662 A250663 A250664

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved