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 A329698 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HD and DU. 1
 1, 1, 2, 3, 5, 8, 13, 22, 37, 64, 111, 195, 346, 618, 1114, 2019, 3683, 6753, 12440, 23018, 42750, 79683, 148993, 279407, 525382, 990325, 1870993, 3542241, 6719450, 12769653, 24308665, 46348192, 88501413, 169228912, 324018531, 621159937, 1192189832, 2290699981, 4406021067 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. LINKS Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019. FORMULA G.f.: (1-t-t^2+2t^3-2t^4-sqrt(1-2t-t^2+2t^3+t^4-4t^5+4t^6))/(2t^3(1-t)^2). EXAMPLE a(3)=3, since we have the following 3 excursions of length 3: UDH, HUD and HHH. CROSSREFS Cf. A329695. Sequence in context: A018152 A293078 A005683 * A173404 A325473 A213710 Adjacent sequences: A329695 A329696 A329697 * A329699 A329700 A329701 KEYWORD nonn,walk AUTHOR Valerie Roitner, Dec 16 2019 STATUS approved

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Last modified February 4 13:27 EST 2023. Contains 360055 sequences. (Running on oeis4.)