A250461 Number of (n+1)X(1+1) 0..1 arrays with nondecreasing min(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.

11, 31, 85, 233, 637, 1741, 4757, 12997, 35509, 97013, 265045, 724117, 1978325, 5404885, 14766421, 40342613, 110218069, 301121365, 822678869, 2247600469, 6140558677, 16776318293, 45833753941, 125220144469, 342107796821

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Nov 14 2018: (Start)

G.f.: x*(11 - 2*x - 8*x^2) / ((1 - x)*(1 - 2*x - 2*x^2)).

a(n) = (-2 + (13-7*sqrt(3))*(1-sqrt(3))^n + (1+sqrt(3))^n*(13+7*sqrt(3))) / 6.

(End)

Example

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

Crossrefs

Column 1 of A250468.

Sequence in context: A269789 A072672 A072673 * A259508 A126365 A082102

Adjacent sequences: A250458 A250459 A250460 * A250462 A250463 A250464

Keyword

nonn

Author

R. H. Hardin, Nov 23 2014

Status

approved