A250880 Number of (3+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.

2002, 6812, 16262, 31928, 55386, 88212, 131982, 188272, 258658, 344716, 448022, 570152, 712682, 877188, 1065246, 1278432, 1518322, 1786492, 2084518, 2413976, 2776442, 3173492, 3606702, 4077648, 4587906, 5139052, 5732662, 6370312, 7053578

Offset

1,1

Links

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

Formula

Empirical: a(n) = (788/3)*n^3 + 744*n^2 + (2218/3)*n + 256.

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

G.f.: 2*x*(1001 - 598*x + 513*x^2 - 128*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..3..3..3..3....3..3..3..2..2....3..3..3..3..3....0..0..0..0..0
..1..2..2..2..2....2..2..2..3..3....2..2..2..2..2....2..2..2..3..3
..0..2..2..2..2....1..1..1..3..3....1..1..1..1..2....1..1..1..3..3
..0..3..3..3..3....0..0..0..2..3....0..2..2..2..3....0..0..0..2..2

Crossrefs

Row 3 of A250877.

Sequence in context: A162238 A162239 A104400 * A154049 A339803 A108116

Adjacent sequences: A250877 A250878 A250879 * A250881 A250882 A250883

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved