

A329700


Number of excursions of length n with Motzkinsteps avoiding the consecutive steps UH, HH and HD.


1



1, 1, 1, 2, 3, 5, 9, 16, 30, 56, 108, 208, 409, 805, 1606, 3211, 6479, 13108, 26691, 54499, 111808, 229983, 474787, 982528, 2039143, 4241187, 8842137, 18469760, 38657209, 81047625, 170212312, 358013615, 754140328, 1590709427, 3359666293, 7104369046, 15040357081, 31875827699
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OFFSET

0,4


COMMENTS

The Motzkin step set is U=(1,1), H=(1,0) and D=(1,1). An excursion is a path starting at (0,0), ending at (n,0) and never crossing the xaxis, i.e., staying at nonnegative altitude.


LINKS

Table of n, a(n) for n=0..37.
Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019.


FORMULA

G.f.: (1+t)*(1t^3sqrt(14t^22t^3+t^6))/(2t^2).


EXAMPLE

a(4)=3 since we have 3 excursions of length 4, namely UUDD, UDUD and HUDH.


CROSSREFS

Cf. A329699.
Sequence in context: A050168 A331966 A072176 * A217282 A047061 A136169
Adjacent sequences: A329697 A329698 A329699 * A329701 A329702 A329703


KEYWORD

nonn,walk


AUTHOR

Valerie Roitner, Dec 16 2019


STATUS

approved



