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 A329669 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DD. 1
 1, 2, 4, 10, 23, 54, 129, 307, 733, 1757, 4213, 10115, 24315, 58481, 140741, 338890, 816304, 1966929, 4740758, 11428851, 27557585, 66458601, 160295262, 386671056, 932839439, 2250660384, 5430575647, 13104191607, 31622724351, 76314992880, 184178642468, 444513674334, 1072865869705 (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^3 - 3*t^2 - sqrt(t^6 + 2*t^5 - 3*t^4 - 6*t^3 - 2*t^2 + 1) - 2*t + 1)/((t^3 + 3*t^2 + t - 1)*t). EXAMPLE a(2)=4 since we have 4 meanders of length two avoiding HH and DD, namely UU, UH, UD and HU. CROSSREFS See also A329666, which counts excursions with same restrictions. Cf. A329667, A329665 (meanders avoiding other sets of step sequences of length 2). Sequence in context: A094987 A189601 A210460 * A191693 A238436 A137681 Adjacent sequences:  A329666 A329667 A329668 * A329670 A329671 A329672 KEYWORD nonn,walk AUTHOR Valerie Roitner, Nov 25 2019 STATUS approved

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Last modified August 17 10:16 EDT 2022. Contains 356187 sequences. (Running on oeis4.)