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A329684 Number of excursions of length n with Motzkin-steps 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 (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 on the x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.

This sequence is periodic with a pre-period 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^2-t^3)/(1-t).

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

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Last modified August 2 05:02 EDT 2021. Contains 346409 sequences. (Running on oeis4.)