

A329669


Number of meanders of length n with Motzkinsteps avoiding the consecutive steps HH and DD.


1



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
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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 xaxis, 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 A137681
Adjacent sequences: A329666 A329667 A329668 * A329670 A329671 A329672


KEYWORD

nonn,walk


AUTHOR

Valerie Roitner, Nov 25 2019


STATUS

approved



