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 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)*(1-t^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2).
EXAMPLE
a(4)=3 since we have 3 excursions of length 4, namely UUDD, UDUD and HUDH.
CROSSREFS
Cf. A329699.
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Dec 16 2019
STATUS
approved