

A329684


Number of excursions of length n with Motzkinsteps forbidding all consecutive steps of length 2 except UD and HH.


3



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


LINKS

Table of n, a(n) for n=0..70.
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

G.f.: (1+t^2t^3)/(1t).


EXAMPLE

a(2)=2 since UD and HH are allowed. For n different from 2, only the excursion H^n is allowed.


CROSSREFS

Cf. A329680, A329682, A329683.
Essentially the same as A294619, A261143 and A141044.
Sequence in context: A299202 A194337 A299912 * A294619 A054977 A272901
Adjacent sequences: A329681 A329682 A329683 * A329685 A329686 A329687


KEYWORD

nonn,walk,easy


AUTHOR

Valerie Roitner, Nov 29 2019


STATUS

approved



