

A329680


Number of excursions of length n with Motzkinsteps consisting only of consecutive steps UH, HD and DU.


3



1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1
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OFFSET

0


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 on the xaxis and never crossing the xaxis, i.e., staying at nonnegative altitude.
This sequence is periodic with a preperiod of length 2 (namely 1, 1) and a period of length 3 (namely 0, 1, 0).


LINKS

Table of n, a(n) for n=0..75.
Index entries for linear recurrences with constant coefficients, signature (0,0,1).


FORMULA

G.f.: (1+tt^4)/(1t^3).
a(n) = A173857(n).  R. J. Mathar, Dec 06 2019


EXAMPLE

For n=3k we have one excursion of this type, namely (UHD)^k. Furthermore, we have a(1)=1, since the excursion H is allowed.


CROSSREFS

Cf. A329682, A329683, A329684.
Cf. A079978.
Sequence in context: A033796 A033790 A033788 * A257234 A055088 A266666
Adjacent sequences: A329677 A329678 A329679 * A329681 A329682 A329683


KEYWORD

nonn,walk,easy


AUTHOR

Valerie Roitner, Nov 29 2019


STATUS

approved



