OFFSET
0,5
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.
FORMULA
G.f.: (t+1)*(1 - t - sqrt(4*t^4 - 4*t^3 + t^2 - 2*t + 1))/(2*t^3).
EXAMPLE
a(4)=2 as one has 2 excursions of length 4, namely: HUHD and UHDH.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 19 2019
STATUS
approved