OFFSET

0,3

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 at (n,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.

LINKS

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+2t^3-2t^4-sqrt(1-2t-t^2+2t^3+t^4-4t^5+4t^6))/(2t^3(1-t)^2).

EXAMPLE

a(3)=3, since we have the following 3 excursions of length 3: UDH, HUD and HHH.

CROSSREFS

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Dec 16 2019

STATUS

approved