A250848 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 min(x(i,j),x(i-1,j)) in the j direction.

1225, 8037, 44797, 223933, 1043885, 4648157, 20067117, 84805533, 353060845, 1454214877, 5943685037, 24157039133, 97778698605, 394573711197, 1588686176557, 6385947864733, 25637459261165, 102830957105117

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) = (18104*4^n - 26144*3^n + 10680*2^n - 644)/12.

Empirical g.f.: x*(1225 - 4213*x + 7302*x^2 - 3992*x^3) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)). -Colin Barker, Nov 21 2018

Example

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

Crossrefs

Column 3 of A250853.

Sequence in context: A350323 A350345 A183665 * A014795 A267297 A151657

Adjacent sequences: A250845 A250846 A250847 * A250849 A250850 A250851

Keyword

nonn

Author

R. H. Hardin, Nov 28 2014

Status

approved