OFFSET

0,4

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)*(1-2t^3-sqrt(1-4t^3-4t^4))/(2t^4).

EXAMPLE

a(4)=3 since we have the following 3 excursions of length 4: UHDH, HUHD and HUDH.

CROSSREFS

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Dec 06 2019

STATUS

approved