

A329683


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


3



1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2
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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 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, 1) and a period of length 1 (namely 2).


LINKS

Table of n, a(n) for n=0..91.


FORMULA

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


EXAMPLE

For n greater or equal three we always have two allowed excursions, namely UH^(n2)D and H^n. For n=0, 1, 2 we have one meander each, namely the empty walk, H and HH.


CROSSREFS

Cf. A329680, A329682, A329684.
Sequence in context: A211665 A065685 A084100 * A130130 A046698 A007395
Adjacent sequences: A329680 A329681 A329682 * A329684 A329685 A329686


KEYWORD

nonn,walk


AUTHOR

Valerie Roitner, Nov 29 2019


STATUS

approved



