

A329668


Number of meanders of length n with Motzkinsteps 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
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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 xaxis, 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)  (1t)*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



