A250870 Number of (n+1) X (1+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.

90, 440, 2002, 8736, 37130, 155080, 640002, 2619056, 10653370, 43144920, 174174002, 701478976, 2820264810, 11324105960, 45425564002, 182089676496, 729520967450, 2921570654200, 11696742970002, 46818352939616

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3); a(n) = (128*4^n - 81*3^n + 1)/3.

Empirical g.f.: 2*x*(45 - 140*x + 96*x^2) / ((1 - x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 22 2018

Example

Some solutions for n=4:
..1..1....0..1....2..2....2..3....0..1....2..1....2..2....1..2....2..2....0..0
..0..0....2..3....0..0....1..2....1..2....1..2....1..1....0..1....1..1....1..1
..0..0....0..1....1..1....0..2....0..2....2..3....1..1....2..3....1..1....2..2
..2..3....0..1....3..3....0..3....0..2....1..3....0..1....0..1....2..3....0..0
..0..1....1..3....0..1....0..3....0..3....0..2....0..1....0..3....2..3....1..1

Crossrefs

Column 1 of A250877.

Sequence in context: A304618 A187300 A237129 * A284845 A203741 A203734

Adjacent sequences: A250867 A250868 A250869 * A250871 A250872 A250873

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved