A250731 Number of (2+1) X (n+1) 0..1 arrays with nondecreasing 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.

18, 46, 110, 257, 596, 1376, 3173, 7310, 16838, 38777, 89300, 205640, 473549, 1090478, 2511134, 5782577, 13315988, 30663728, 70611701, 162602894, 374438006, 862246697, 1985560724, 4572300824, 10528983005, 24245885486, 55832834510

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(18 + 10*x - 18*x^2 - x^3) / ((1 - x)*(1 - x - 3*x^2)). - Colin Barker, Nov 16 2018

Example

Some solutions for n=4:
..0..0..0..0..1....0..0..0..0..1....0..0..0..0..0....1..0..0..0..0
..0..1..0..0..1....0..1..0..0..1....0..0..0..0..0....0..1..0..0..1
..1..0..1..0..1....1..0..1..1..1....1..0..0..1..0....1..0..1..0..1

Crossrefs

Row 2 of A250729.

Sequence in context: A130414 A108642 A250784 * A353209 A203596 A305171

Adjacent sequences: A250728 A250729 A250730 * A250732 A250733 A250734

Keyword

nonn

Author

R. H. Hardin, Nov 27 2014

Status

approved