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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)
OFFSET

0,2

COMMENTS

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.

LINKS

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).

Andrei Asinowski, Cyril Banderier, Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, (2019).

FORMULA

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

EXAMPLE

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A004149.

Sequence in context: A206741 A167750 A329276 * A188460 A111099 A000632

Adjacent sequences:  A308432 A308433 A308434 * A308436 A308437 A308438

KEYWORD

nonn

AUTHOR

Andrei Asinowski, May 27 2019

STATUS

approved

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Last modified November 27 18:22 EST 2020. Contains 338683 sequences. (Running on oeis4.)