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.
LINKS
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^3 + t^4.
EXAMPLE
We only have the following four excursions of this type: the empty walk, H, UHD and UHDH.
MATHEMATICA
PadRight[#, 105] &@ CoefficientList[Series[1 + x + x^3 + x^4, {x, 0, 105}], x] (* Michael De Vlieger, Dec 16 2019 *)
CROSSREFS
KEYWORD
nonn,walk,easy
AUTHOR
Valerie Roitner, Dec 16 2019
STATUS
approved