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 A329700 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD. 1

%I

%S 1,1,1,2,3,5,9,16,30,56,108,208,409,805,1606,3211,6479,13108,26691,

%T 54499,111808,229983,474787,982528,2039143,4241187,8842137,18469760,

%U 38657209,81047625,170212312,358013615,754140328,1590709427,3359666293,7104369046,15040357081,31875827699

%N Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD.

%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)*(1-t^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2).

%e a(4)=3 since we have 3 excursions of length 4, namely UUDD, UDUD and HUDH.

%Y Cf. A329699.

%K nonn,walk

%O 0,4

%A _Valerie Roitner_, Dec 16 2019

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Last modified March 22 11:07 EDT 2023. Contains 361423 sequences. (Running on oeis4.)