A250607 Number of (n+1) X (4+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.

120, 290, 592, 1126, 2092, 3890, 7320, 13982, 27076, 53002, 104560, 207350, 412572, 822626, 1642312, 3281230, 6558580, 13112762, 26220576, 52435622, 104865100, 209723410, 419439352, 838870526, 1677732132, 3355454570, 6710898640

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) = 100*2^(n-1) + 16*n^2 + 22*n - 18.

Empirical g.f.: 2*x*(60 - 155*x + 111*x^2 - 32*x^3) / ((1 - x)^3*(1 - 2*x)). - Colin Barker, Nov 15 2018

Example

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

Crossrefs

Column 4 of A250611.

Sequence in context: A070856 A211467 A257712 * A076579 A345350 A121898

Adjacent sequences: A250604 A250605 A250606 * A250608 A250609 A250610

Keyword

nonn

Author

R. H. Hardin, Nov 26 2014

Status

approved