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 A329699 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HU and HH. 1
 1, 1, 1, 1, 2, 3, 6, 10, 20, 36, 72, 136, 273, 532, 1074, 2137, 4342, 8766, 17925, 36574, 75234, 154749, 320038, 662490, 1376653, 2864534, 5977603, 12492157, 26165052, 54882573, 115329739, 242683876, 511456452, 1079252975, 2280413318, 4823955728, 10216401353, 21659426346 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2). G.f. A(x) satisfies: A(x) = x + 1 / (1 - x^2 * A(x)). - Ilya Gutkovskiy, Nov 03 2021 EXAMPLE a(5)=3 since we have the following 3 excursions of length 5: UUDDH, UUHDH and UDUDH. CROSSREFS Cf. A329700. Sequence in context: A006606 A120421 A005418 * A002215 A007562 A345973 Adjacent sequences: A329696 A329697 A329698 * A329700 A329701 A329702 KEYWORD nonn,walk AUTHOR Valerie Roitner, Dec 16 2019 STATUS approved

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Last modified December 9 04:13 EST 2022. Contains 358698 sequences. (Running on oeis4.)