A250858 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 min(x(i,j),x(i-1,j)) in the j direction.

233683, 1280447, 4648157, 13263136, 32201019, 69543783, 137379337, 252943672, 439905571, 729793879, 1163567333, 1793326952, 2684170987, 3916192431, 5586619089, 7812096208, 10731111667, 14506563727, 19328471341, 25416827024

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..60

Formula

Empirical: a(n) = 198*n^6 + (35807/12)*n^5 + (204911/12)*n^4 + (214827/4)*n^3 + (998209/12)*n^2 + (180451/3)*n + 16384.

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

G.f.: x*(233683 - 355334*x + 592371*x^2 - 563481*x^3 + 333624*x^4 - 114687*x^5 + 16384*x^6) / (1 - x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.

(End)

Example

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

Crossrefs

Row 6 of A250853.

Sequence in context: A250682 A238500 A224656 * A233902 A202938 A109690

Adjacent sequences: A250855 A250856 A250857 * A250859 A250860 A250861

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved