The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

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