OFFSET
0,2
COMMENTS
The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e., staying at nonnegative altitude.
FORMULA
G.f.: (1/2)*(-t^3 - 3*t^2 - sqrt(t^6 + 2*t^5 - 3*t^4 - 6*t^3 - 2*t^2 + 1) - 2*t + 1)/((t^3 + 3*t^2 + t - 1)*t).
EXAMPLE
a(2)=4 since we have 4 meanders of length two avoiding HH and DD, namely UU, UH, UD and HU.
CROSSREFS
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 25 2019
STATUS
approved