%N Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU and HH.
%C 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.
%H Andrei Asinowski, Cyril Banderier, and Valerie Roitner, <a href="https://lipn.univ-paris13.fr/~banderier/Papers/several_patterns.pdf">Generating functions for lattice paths with several forbidden patterns</a>, preprint, 2019.
%F G.f.: (1+t^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2).
%e a(5)=3 since we have the following 3 excursions of length 5: UUDDH, UUHDH and UDUDH.
%Y Cf. A329700.
%A _Valerie Roitner_, Dec 16 2019