A250606 Number of (n+1) X (3+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.

57, 140, 297, 592, 1153, 2236, 4353, 8528, 16809, 33292, 66169, 131824, 263025, 525308, 1049745, 2098480, 4195801, 8390284, 16779081, 33556496, 67111137, 134220220, 268438177, 536873872, 1073745033, 2147487116, 4294971033

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) = 64*2^(n-1) + 5*n^2 + 4*n -16.

Empirical g.f.: x*(57 - 145*x + 110*x^2 - 32*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 15 2018

Example

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

Crossrefs

Column 3 of A250611.

Sequence in context: A140367 A044308 A044689 * A356423 A044389 A044770

Adjacent sequences: A250603 A250604 A250605 * A250607 A250608 A250609

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved