A250759 Number of (4+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.

1029, 2361, 4239, 6663, 9633, 13149, 17211, 21819, 26973, 32673, 38919, 45711, 53049, 60933, 69363, 78339, 87861, 97929, 108543, 119703, 131409, 143661, 156459, 169803, 183693, 198129, 213111, 228639, 244713, 261333, 278499, 296211, 314469

Offset

1,1

Links

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

Formula

Empirical: a(n) = 273*n^2 + 513*n + 243.

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

G.f.: 3*x*(343 - 242*x + 81*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....2..2..2..2..2....0..0..0..0..0....1..1..1..1..1
..2..2..2..2..2....0..0..0..0..0....0..0..1..1..1....0..0..1..1..1
..0..0..0..1..1....0..0..0..0..0....0..0..1..1..1....1..1..2..2..2
..1..1..1..2..2....2..2..2..2..2....1..1..2..2..2....0..0..1..1..1
..0..1..1..2..2....1..1..1..2..2....0..0..1..2..2....0..0..1..1..2

Crossrefs

Row 4 of A250755.

Sequence in context: A252772 A168189 A045031 * A260607 A298910 A256075

Adjacent sequences: A250756 A250757 A250758 * A250760 A250761 A250762

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved