A329670 Number of excursions of length n with Motzkin-steps allowing only consecutive steps UH and HD.

1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0

Comments

The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). An excursion is a path starting at (0,0), ending on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.

Links

Table of n, a(n) for n=0..96.

Formula

G.f.: 1+t+t^3.

Example

The only excursions of this type are the empty walk, H and UHD.

Crossrefs

Sequence in context: A309970 A039963 A267537 * A183919 A355449 A058840

Adjacent sequences: A329667 A329668 A329669 * A329671 A329672 A329673

Keyword

nonn,walk

Author

Valerie Roitner, Nov 25 2019

Status

approved