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.
This sequence is periodic with a pre-period of length 2 (namely 1, 1) and a period of length 3 (namely 0, 1, 0).
LINKS
FORMULA
G.f.: (1+t-t^4)/(1-t^3).
a(n) = A173857(n). - R. J. Mathar, Dec 06 2019
EXAMPLE
For n=3k we have one excursion of this type, namely (UHD)^k. Furthermore, we have a(1)=1, since the excursion H is allowed.
CROSSREFS
KEYWORD
nonn,walk,easy
AUTHOR
Valerie Roitner, Nov 29 2019
STATUS
approved