

A329675


Number of meanders of length n with Motzkinsteps 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
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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..33.


FORMULA

G.f.: (12*tt^2+t^3sqrt(t^6+2*t^53*t^46*t^32*t^2+1))/(2*t*(12*tt^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



