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A329699 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU and HH. 1

%I

%S 1,1,1,1,2,3,6,10,20,36,72,136,273,532,1074,2137,4342,8766,17925,

%T 36574,75234,154749,320038,662490,1376653,2864534,5977603,12492157,

%U 26165052,54882573,115329739,242683876,511456452,1079252975,2280413318,4823955728,10216401353,21659426346

%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.

%K nonn,walk

%O 0,5

%A _Valerie Roitner_, Dec 16 2019

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