A250658 Number of (4+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.

79, 142, 221, 316, 427, 554, 697, 856, 1031, 1222, 1429, 1652, 1891, 2146, 2417, 2704, 3007, 3326, 3661, 4012, 4379, 4762, 5161, 5576, 6007, 6454, 6917, 7396, 7891, 8402, 8929, 9472, 10031, 10606, 11197, 11804, 12427, 13066, 13721, 14392, 15079, 15782

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*n^2 + 39*n + 32.

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

G.f.: x*(79 - 95*x + 32*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..0..0....1..1..1..0..0
..1..1..1..1..1....1..1..1..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..1....0..0..0..0..0
..1..1..1..1..1....0..0..0..0..0....0..0..0..0..1....0..1..1..1..1
..0..1..1..1..1....0..0..0..0..0....0..0..0..0..1....0..1..1..1..1

Crossrefs

Row 4 of A250656.

Sequence in context: A349234 A141997 A107184 * A029703 A142082 A031890

Adjacent sequences: A250655 A250656 A250657 * A250659 A250660 A250661

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved