OFFSET
0,7
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.: (1+t)*(1-sqrt(1-4t^3))/(2t^3).
D-finite with recurrence: +(n+3)*a(n) +(n+1)*a(n-1) +2*(-2*n+3)*a(n-3) +2*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Feb 21 2020
EXAMPLE
a(6)=2 since we have the following two excursions of length 6: UHDUHD and UHUHDD.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 29 2019
STATUS
approved