A250872 Number of (n+1) X (3+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.

678, 3442, 16262, 73122, 317878, 1350002, 5640102, 23289922, 95366678, 388124562, 1572545542, 6350471522, 25583049078, 102876275122, 413138516582, 1657456673922, 6644539237078, 26622304009682, 106621676097222

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) = (1168*4^n - 1026*3^n + 216*2^n + 8)/3.

Empirical g.f.: 2*x*(339 - 1669*x + 2786*x^2 - 1464*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). - Colin Barker, Nov 22 2018

Example

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

Crossrefs

Column 3 of A250877.

Sequence in context: A158385 A251836 A251830 * A186127 A097771 A121105

Adjacent sequences: A250869 A250870 A250871 * A250873 A250874 A250875

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved