A250881 Number of (4+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.

8736, 30360, 73122, 144248, 250964, 400496, 600070, 856912, 1178248, 1571304, 2043306, 2601480, 3253052, 4005248, 4865294, 5840416, 6937840, 8164792, 9528498, 11036184, 12695076, 14512400, 16495382, 18651248, 20987224, 23510536, 26228410

Offset

1,1

Links

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

Formula

Empirical: a(n) = (3613/3)*n^3 + 3343*n^2 + (9494/3)*n + 1024.

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

G.f.: 2*x*(4368 - 2292*x + 2049*x^2 - 512*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=4:
..2..2..2..2..2....0..0..0..0..0....0..0..0..0..0....2..2..2..2..2
..2..2..2..2..2....3..3..3..3..3....1..1..1..1..1....3..3..3..3..3
..0..0..0..0..0....1..2..2..2..2....3..3..3..3..3....1..1..1..1..1
..0..0..0..1..1....0..1..2..3..3....1..1..1..1..2....3..3..3..3..3
..1..1..1..2..2....0..1..2..3..3....0..0..1..1..2....1..1..3..3..3

Crossrefs

Row 4 of A250877.

Sequence in context: A214171 A067867 A234734 * A234707 A257748 A110077

Adjacent sequences: A250878 A250879 A250880 * A250882 A250883 A250884

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved