

A329693


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


2



1, 1, 1, 2, 2, 3, 4, 6, 9, 13, 21, 31, 50, 78, 123, 200, 315, 517, 831, 1355, 2224, 3620, 5995, 9835, 16291, 27004, 44734, 74625, 124078, 207437, 346765, 580418, 974358, 1634622, 2750502, 4628758, 7800544, 13164287, 22223486, 37579843, 63571333, 107659948, 182479796, 309478532
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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..43.


FORMULA

G.f.: (1+t)*(1+tt^2t^4(1+t)*sqrt(12t^22t^3+t^42t^5+t^6))/(2t^3).


EXAMPLE

a(5)=3 since we have 3 excursions of length 5, namely UUDDH, HUUDD and UDHUD.


CROSSREFS

Cf. A329691, A329692.
Sequence in context: A212264 A174650 A107293 * A329976 A329703 A001611
Adjacent sequences: A329690 A329691 A329692 * A329694 A329695 A329696


KEYWORD

nonn,walk


AUTHOR

Valerie Roitner, Dec 06 2019


STATUS

approved



