A329679 Number of excursions of length n with Motzkin-steps consisting only of consecutive steps UH, UD, HD and DH.

1, 1, 1, 2, 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

Offset

0,4

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.

Index entries for linear recurrences with constant coefficients, signature (1).

Formula

G.f.: 1 + t + t^2 + 2t^3 + t^4.

Example

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

Crossrefs

Cf. A329670, A329677, A329678 (other Motzkin excursions avoiding certain consecutive steps such that the sequence counting them has growth rate zero).

Sequence in context: A230093 A066288 A033322 * A130713 A236619 A355627

Adjacent sequences: A329676 A329677 A329678 * A329680 A329681 A329682

Keyword

nonn,walk,easy

Author

Valerie Roitner, Dec 16 2019

Status

approved