A329678 Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UD and DH.

1, 1, 1, 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.

Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019.

Formula

G.f.: 1 + t + t^2 + t^3.

Example

We only have the following four excursions of this type: the empty walk, H, UD and UDH.

Crossrefs

Cf. A329670, A329677, A329679 (other Motzkin excursions avoiding certain consecutive steps such that the sequence counting them has growth rate zero).

Sequence in context: A293163 A359832 A267871 * A359942 A266434 A025447

Adjacent sequences: A329675 A329676 A329677 * A329679 A329680 A329681

Keyword

nonn,walk,easy

Author

Valerie Roitner, Dec 16 2019

Status

approved