A250605 Number of (n+1) X (2+1) 0..1 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.

26, 64, 140, 290, 586, 1172, 2336, 4654, 9278, 18512, 36964, 73850, 147602, 295084, 590024, 1179878, 2359558, 4718888, 9437516, 18874738, 37749146, 75497924, 150995440, 301990430, 603980366, 1207960192, 2415919796, 4831838954

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).

Empirical: a(n) = 36*2^(n-1) + n^2 - n - 10.

Empirical g.f.: 2*x*(13 - 33*x + 27*x^2 - 8*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 15 2018

Example

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

Crossrefs

Column 2 of A250611.

Sequence in context: A321023 A064867 A228512 * A020155 A063304 A199849

Adjacent sequences: A250602 A250603 A250604 * A250606 A250607 A250608

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved