A329669 Number of meanders of length n with Motzkin-steps avoiding the consecutive steps HH and DD.

1, 2, 4, 10, 23, 54, 129, 307, 733, 1757, 4213, 10115, 24315, 58481, 140741, 338890, 816304, 1966929, 4740758, 11428851, 27557585, 66458601, 160295262, 386671056, 932839439, 2250660384, 5430575647, 13104191607, 31622724351, 76314992880, 184178642468, 444513674334, 1072865869705

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..32.

Formula

G.f.: (1/2)*(-t^3 - 3*t^2 - sqrt(t^6 + 2*t^5 - 3*t^4 - 6*t^3 - 2*t^2 + 1) - 2*t + 1)/((t^3 + 3*t^2 + t - 1)*t).

Example

a(2)=4 since we have 4 meanders of length two avoiding HH and DD, namely UU, UH, UD and HU.

Crossrefs

See also A329666, which counts excursions with same restrictions.

Cf. A329667, A329665 (meanders avoiding other sets of step sequences of length 2).

Sequence in context: A094987 A189601 A210460 * A191693 A238436 A366229

Adjacent sequences: A329666 A329667 A329668 * A329670 A329671 A329672

Keyword

nonn,walk

Author

Valerie Roitner, Nov 25 2019

Status

approved