A250816 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 min(x(i,j),x(i-1,j)) in the j direction.

1389, 4321, 10233, 20631, 37333, 62469, 98481, 148123, 214461, 300873, 411049, 548991, 719013, 925741, 1174113, 1469379, 1817101, 2223153, 2693721, 3235303, 3854709, 4559061, 5355793, 6252651, 7257693, 8379289, 9626121, 11007183

Offset

1,1

Links

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

Formula

Empirical: a(n) = 13*n^4 + 121*n^3 + 439*n^2 + 573*n + 243.

Conjectures from Colin Barker, Nov 21 2018: (Start)

G.f.: x*(1389 - 2624*x + 2518*x^2 - 1214*x^3 + 243*x^4) / (1 - x)^5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

(End)

Example

Some solutions for n=4:
..0..0..0..0..0....2..2..1..1..0....2..2..2..1..0....2..2..2..2..1
..0..0..0..2..2....0..0..0..0..0....0..0..0..0..1....0..0..0..0..0
..0..0..0..2..2....2..2..2..2..2....0..0..0..1..2....1..1..1..1..1
..0..0..0..2..2....0..0..1..1..1....0..0..0..1..2....1..1..1..2..2
..0..0..0..2..2....1..1..2..2..2....0..0..0..1..2....1..1..1..2..2

Crossrefs

Row 4 of A250812.

Sequence in context: A253490 A253451 A281164 * A031983 A249970 A069422

Adjacent sequences: A250813 A250814 A250815 * A250817 A250818 A250819

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved