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A329665 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU. 3
1, 2, 3, 6, 11, 20, 38, 72, 136, 260, 499, 958, 1847, 3572, 6917, 13422, 26097, 50808, 99049, 193354, 377857, 739148, 1447292, 2836316, 5562774, 10918180, 21444029, 42143986, 82874681, 163060540, 320996342, 632211192, 1245727488, 2455674532, 4842782497, 9554018554, 18855375593, 37224944572 (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..37.

FORMULA

G.f.: ((-t-1)*sqrt(4*t^4-4*t^3+t^2-2*t+1)-2*t^3-3*t^2+1)/(4*t^3-2*t^2).

EXAMPLE

a(3)=6 as one has 6 meanders of length 3, namely: UUU, UUH, UHU, UHD, HUU, HUH.

CROSSREFS

Cf. A308435 (avoiding UD and DU), A329666 (avoiding UU and HH).

Cf. A329664.

Sequence in context: A318910 A141435 A096080 * A143658 A005230 A030037

Adjacent sequences:  A329662 A329663 A329664 * A329666 A329667 A329668

KEYWORD

nonn,walk

AUTHOR

Valerie Roitner, Nov 19 2019

STATUS

approved

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Last modified August 17 00:01 EDT 2022. Contains 356180 sequences. (Running on oeis4.)