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.: -(1-3*t-t^2-sqrt(1-2*t-t^2-2*t^3+t^4))/(2*t*(1-2*t-2*t^2)).
D-finite with recurrence (n+1)*a(n) +(-4*n-1)*a(n-1) +(n-2)*a(n-2) +(4*n+1)*a(n-3) +(7*n-23)*a(n-4) +2*(n-2)*a(n-5) +2*(-n+5)*a(n-6)=0. - R. J. Mathar, Jan 25 2023
EXAMPLE
a(2)=5 since we have 5 meanders of length 2 avoiding DD, namely UU, UH, UD, HU and HH.
CROSSREFS
Cf. A004148 (shifted by 1) which counts excursions avoiding consecutive DD steps.
KEYWORD
nonn,walk
AUTHOR
Valerie Roitner, Nov 26 2019
STATUS
approved