A250882 Number of (5+1) X (n+1) 0..3 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.

37130, 131068, 317878, 629528, 1097986, 1755220, 2633198, 3763888, 5179258, 6911276, 8991910, 11453128, 14326898, 17645188, 21439966, 25743200, 30586858, 36002908, 42023318, 48680056, 56005090, 64030388, 72787918, 82309648, 92627546

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..156

Formula

Empirical: a(n) = 5328*n^3 + 14468*n^2 + 13238*n + 4096.

Conjectures from Colin Barker, Nov 22 2018: (Start)

G.f.: 2*x*(18565 - 8726*x + 8193*x^2 - 2048*x^3) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

Some solutions for n=2:
..1..1..1....2..2..2....1..1..1....2..2..2....0..0..1....2..3..3....0..0..0
..2..2..2....0..0..0....1..1..1....3..3..3....1..1..2....1..2..3....2..3..3
..1..1..1....3..3..3....2..2..2....1..1..2....2..2..3....1..2..3....0..1..1
..3..3..3....2..2..2....2..2..2....0..0..2....0..1..2....1..2..3....2..3..3
..2..2..2....0..1..1....3..3..3....1..1..3....1..2..3....0..2..3....1..3..3
..0..1..2....0..2..3....2..3..3....0..0..2....0..1..2....0..2..3....1..3..3

Crossrefs

Row 5 of A250877.

Sequence in context: A206051 A279862 A112728 * A219363 A254564 A151630

Adjacent sequences: A250879 A250880 A250881 * A250883 A250884 A250885

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved