A329665 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps UD, HH and DU.

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

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