A250871 Number of (n+1) X (2+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.

288, 1456, 6812, 30360, 131068, 553736, 2304492, 9488920, 38773148, 157554216, 637620172, 2572727480, 10357724028, 41631485896, 167128007852, 670318814040, 2686696783708, 10763054076776, 43101021851532, 172550513476600

Offset

1,1

Links

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

Formula

Empirical: a(n) = 10*a(n-1) - 35*a(n-2) + 50*a(n-3) - 24*a(n-4); a(n) = (472*4^n - 378*3^n + 54*2^n + 2)/3.

Empirical g.f.: 4*x*(72 - 356*x + 583*x^2 - 300*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 22 2018

Example

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

Crossrefs

Column 2 of A250877.

Sequence in context: A281236 A237369 A280936 * A128392 A296784 A235078

Adjacent sequences: A250868 A250869 A250870 * A250872 A250873 A250874

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved