OFFSET
0,9
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.
FORMULA
G.f.: (1+t^2+t^3-sqrt(1-2t^2-2t^3+t^4-2t^5+t^6))/(2t^2).
EXAMPLE
a(8)=3 since we have the following 3 excursions of length 8: UUHDDUHD, UHDUUHDD and UUHDUHDD.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Dec 06 2019
STATUS
approved