A250576 Number of (n+1) X (1+1) 0..1 arrays with nondecreasing max(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.

10, 24, 55, 125, 282, 635, 1428, 3210, 7214, 16211, 36427, 81852, 183921, 413268, 928606, 2086560, 4688459, 10534873, 23671646, 53189707, 119516188, 268550438, 603427358, 1355888967, 3046654855, 6845771320, 15382308529, 34563733524

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 2*a(n-3) +a(n-4).

Empirical g.f.: x*(10 - 6*x - 7*x^2 + 4*x^3) / ((1 - x)*(1 - 2*x - x^2 + x^3)). - Colin Barker, Nov 15 2018

Example

Some solutions for n=6:
..0..0....1..1....1..1....0..1....0..0....1..1....0..0....0..0....0..0....1..1
..1..1....0..1....0..1....1..1....1..1....0..1....0..0....0..0....0..0....0..1
..1..1....1..0....0..1....1..1....1..1....1..1....1..1....1..0....0..0....0..1
..0..1....0..1....1..1....0..1....1..1....0..1....0..1....0..1....1..1....1..1
..0..1....1..0....1..1....0..1....0..1....0..1....1..0....1..1....1..1....1..1
..0..1....0..1....0..1....1..1....1..0....0..1....0..1....1..1....0..1....1..1
..1..1....1..0....1..0....1..1....0..1....1..0....1..1....0..1....1..0....0..1

Crossrefs

Column 1 of A250583.

Sequence in context: A352283 A058504 A250798 * A126911 A223408 A261807

Adjacent sequences: A250573 A250574 A250575 * A250577 A250578 A250579

Keyword

nonn

Author

R. H. Hardin, Nov 25 2014

Status

approved