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A329675 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD and HH. 1
1, 2, 3, 6, 12, 24, 50, 105, 221, 471, 1008, 2164, 4669, 10102, 21909, 47642, 103801, 226549, 495284, 1084318, 2376902, 5216543, 11460725, 25203497, 55475172, 122205631, 269408827, 594343482, 1312035579, 2898123874, 6405224773, 14163866716, 31336109418, 69360335726 (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-t^2+t^3-sqrt(t^6+2*t^5-3*t^4-6*t^3-2*t^2+1))/(2*t*(1-2*t-t^2+t^3)).

EXAMPLE

a(3)=6 since we have 6 meanders of length 3, namely UUU, UUH, UHU, UHD, HUU and HUH.

CROSSREFS

Cf. A329676 which counts excursions avoiding consecutive UD and HH.

Sequence in context: A042950 A035055 A119559 * A045761 A187741 A216632

Adjacent sequences:  A329672 A329673 A329674 * A329676 A329677 A329678

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Nov 29 2019

STATUS

approved

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Last modified August 3 08:10 EDT 2020. Contains 336197 sequences. (Running on oeis4.)