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A308435 Peak- and valleyless Motzkin meanders. 1
1, 2, 4, 9, 20, 45, 102, 233, 535, 1234, 2857, 6636, 15456, 36085, 84424, 197883, 464585, 1092348, 2571770, 6062109, 14305022, 33789777, 79887365, 189031914, 447639473, 1060798484, 2515512091, 5968826698, 14171068794, 33662866431, 80005478832, 190237068767, 452548530595 (list; graph; refs; listen; history; text; internal format)



a(n) is the number of Motzkin meanders that avoid UD and DU. A Motzkin meander is a lattice paths that starts at (0,0), uses steps U=1, H=0, D=-1, and never goes below the x-axis.


Table of n, a(n) for n=0..32.

Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Algorithmica (2019).

Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic Combinatorics of Lattice Paths with Forbidden Patterns: Asymptotic Aspects and Borges's Theorem, 29th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2018).


G.f.: -(1+t-sqrt((1-t^4)/(1-2*t-t^2)))/(2*t^2).


For n=3, the a(3)=9 such meanders are UUU, UUH, UHU, UHH, UHD, HUU, HUH, HHU, HHH.


CoefficientList[Series[-(1+x-Sqrt[(1-x^4)/(1-2*x-x^2)])/(2*x^2), {x, 0, 40}], x] (* Vaclav Kotesovec, Jun 05 2019 *)


(PARI) my(t='t + O('t^40)); Vec(-(1+t-sqrt((1-t^4)/(1-2*t-t^2)))/(2*t^2)) \\ Michel Marcus, May 27 2019


Cf. A004149.

Sequence in context: A206741 A167750 A329276 * A188460 A111099 A000632

Adjacent sequences:  A308432 A308433 A308434 * A308436 A308437 A308438




Andrei Asinowski, May 27 2019



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Last modified December 13 09:58 EST 2019. Contains 329968 sequences. (Running on oeis4.)