login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..33.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 31 16:29 EDT 2020. Contains 334748 sequences. (Running on oeis4.)