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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 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.)