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 A329668 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DU. 1
 1, 2, 4, 9, 18, 38, 81, 171, 366, 787, 1693, 3661, 7938, 17240, 37540, 81892, 178907, 391483, 857769, 1881618, 4132225, 9083823, 19986954, 44014447, 97002134, 213933655, 472137851, 1042626752, 2303780392, 5093189194, 11265742842, 24930884645, 55196469010, 122255756284 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The Motzkin step set is U=(1,1), H=(1,0) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e., staying at nonnegative altitude. LINKS FORMULA G.f.: -(1/2)*(t+1)*((t^3 - t^2 - 2*t + 1)*(t+1) - (1-t)*sqrt((t^3 - t^2 - 2*t + 1)*(t^3 + 3*t^2 + 2*t + 1)))/((t^3 - t^2 - 2*t + 1)*t^2). EXAMPLE a(3)=9 as one has 9 meanders of length 3, namely: UUU, UUH, UUD, UDH, UHU, UHD, HUU, HUD and HUH. CROSSREFS Cf. A329666, which counts excursions with same restrictions. Sequence in context: A079580 A327739 A018000 * A320222 A036610 A219755 Adjacent sequences:  A329665 A329666 A329667 * A329669 A329670 A329671 KEYWORD nonn,walk AUTHOR Valerie Roitner, Nov 25 2019 STATUS approved

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Last modified August 17 03:53 EDT 2022. Contains 356184 sequences. (Running on oeis4.)