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A329698
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Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HD and DU.
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1
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..38.
Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019.
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FORMULA
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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).
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EXAMPLE
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a(3)=3, since we have the following 3 excursions of length 3: UDH, HUD and HHH.
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CROSSREFS
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Cf. A329695.
Sequence in context: A018152 A293078 A005683 * A173404 A325473 A213710
Adjacent sequences: A329695 A329696 A329697 * A329699 A329700 A329701
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KEYWORD
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nonn,walk
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AUTHOR
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Valerie Roitner, Dec 16 2019
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STATUS
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approved
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