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A329683 Number of excursions of length n with Motzkin-steps 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 (list; graph; refs; listen; history; text; internal format)
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 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, 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)/(1-t).

EXAMPLE

For n greater or equal three we always have two allowed excursions, namely UH^(n-2)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

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Last modified July 31 02:33 EDT 2021. Contains 346367 sequences. (Running on oeis4.)