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 A329700 Number of excursions of length n with Motzkin-steps avoiding the consecutive steps UH, HH and HD. 1
 1, 1, 1, 2, 3, 5, 9, 16, 30, 56, 108, 208, 409, 805, 1606, 3211, 6479, 13108, 26691, 54499, 111808, 229983, 474787, 982528, 2039143, 4241187, 8842137, 18469760, 38657209, 81047625, 170212312, 358013615, 754140328, 1590709427, 3359666293, 7104369046, 15040357081, 31875827699 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 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)*(1-t^3-sqrt(1-4t^2-2t^3+t^6))/(2t^2). EXAMPLE a(4)=3 since we have 3 excursions of length 4, namely UUDD, UDUD and HUDH. CROSSREFS Cf. A329699. Sequence in context: A050168 A331966 A072176 * A217282 A047061 A136169 Adjacent sequences: A329697 A329698 A329699 * A329701 A329702 A329703 KEYWORD nonn,walk AUTHOR Valerie Roitner, Dec 16 2019 STATUS approved

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Last modified January 28 10:39 EST 2023. Contains 359859 sequences. (Running on oeis4.)