A329668 - OEIS

A329668

Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DU.

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 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