

A329698


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


1



1, 1, 2, 3, 5, 8, 13, 22, 37, 64, 111, 195, 346, 618, 1114, 2019, 3683, 6753, 12440, 23018, 42750, 79683, 148993, 279407, 525382, 990325, 1870993, 3542241, 6719450, 12769653, 24308665, 46348192, 88501413, 169228912, 324018531, 621159937, 1192189832, 2290699981, 4406021067
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


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..38.
Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019.


FORMULA

G.f.: (1tt^2+2t^32t^4sqrt(12tt^2+2t^3+t^44t^5+4t^6))/(2t^3(1t)^2).


EXAMPLE

a(3)=3, since we have the following 3 excursions of length 3: UDH, HUD and HHH.


CROSSREFS

Cf. A329695.
Sequence in context: A018152 A293078 A005683 * A173404 A325473 A213710
Adjacent sequences: A329695 A329696 A329697 * A329699 A329700 A329701


KEYWORD

nonn,walk


AUTHOR

Valerie Roitner, Dec 16 2019


STATUS

approved



