A250883 Number of (6+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.

155080, 553736, 1350002, 2681528, 4685964, 7500960, 11264166, 16113232, 22185808, 29619544, 38552090, 49121096, 61464212, 75719088, 92023374, 110514720, 131330776, 154609192, 180487618, 209103704, 240595100, 275099456

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..47

Formula

Empirical: a(n) = (68825/3)*n^3 + 61155*n^2 + (163798/3)*n + 16384.

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

G.f.: 2*x*(77540 - 33292*x + 32769*x^2 - 8192*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=1:
..0..0....2..2....2..2....0..0....2..2....2..2....2..2....2..2....1..1....0..0
..2..2....0..0....3..3....0..0....3..3....0..2....1..1....2..2....2..2....2..2
..0..0....0..1....0..0....1..1....2..2....1..3....3..3....1..2....0..0....1..1
..3..3....0..1....2..2....3..3....0..0....0..2....2..2....1..2....0..0....3..3
..3..3....1..2....3..3....3..3....2..3....1..3....2..2....1..2....0..1....3..3
..1..1....0..2....0..0....1..3....0..1....1..3....0..2....0..1....0..1....1..1
..3..3....0..2....1..1....0..2....0..2....0..3....0..2....1..2....1..2....0..3

Crossrefs

Row 6 of A250877.

Sequence in context: A101767 A235220 A282163 * A233816 A050520 A049443

Adjacent sequences: A250880 A250881 A250882 * A250884 A250885 A250886

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved