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A329680 Number of excursions of length n with Motzkin-steps 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 (list; graph; refs; listen; history; text; internal format)
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 x-axis and never crossing the x-axis, i.e., staying at nonnegative altitude.

This sequence is periodic with a pre-period 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+t-t^4)/(1-t^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

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Last modified September 20 10:51 EDT 2021. Contains 347584 sequences. (Running on oeis4.)