The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A329703 Number of meanders of length n with Dyck-steps avoiding the consecutive steps UDU and DUD. 0
 1, 1, 2, 2, 3, 4, 6, 9, 14, 21, 33, 50, 79, 121, 192, 296, 471, 730, 1164, 1812, 2894, 4521, 7230, 11328, 18135, 28485, 45642, 71844, 115203, 181674, 291504, 460443, 739212, 1169283, 1878123, 2974574, 4779865, 7578937, 12183300, 19337489, 31096041, 49401526, 79465563, 126350742 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The Dyck step set is U=(1,1) and D=(1,-1). A meander is a path starting at (0,0) and never crossing the x-axis, i.e., staying at nonnegative altitude. LINKS Andrei Asinowski, Cyril Banderier, and Valerie Roitner, Generating functions for lattice paths with several forbidden patterns, preprint, 2019. FORMULA G.f.: (1 - t - t^2 - t^3 + t^4 + t^5 - (1+t)*sqrt(t^8-2*t^6-t^4-2*t^2+1))/(2*t*(t^2+t-1)). D-finite with recurrence: (n+1)*a(n) +(n-2)*a(n-1) -2*n*a(n-2) +(-2*n+3)*a(n-3) +(-n+2)*a(n-4) +(-n+4)*a(n-5) +(-2*n+13)*a(n-6) +2*(-n+9)*a(n-7) +(n-10)*a(n-8) +(n-11)*a(n-9)=0. - R. J. Mathar, Jan 27 2020 EXAMPLE a(5)=4 since we have 4 meanders of length 5, namely UUUUU, UUUUD, UUUDD and UUDDU. MATHEMATICA CoefficientList[Series[(1 - x - x^2 - x^3 + x^4 + x^5 - (1 + x)*Sqrt[x^8 - 2 x^6 - x^4 - 2 x^2 + 1])/(2 x (x^2 + x - 1)), {x, 0, 43}], x] (* Michael De Vlieger, Dec 16 2019 *) PROG (PARI) Vec((1 - x - x^2 - x^3 + x^4 + x^5 - (1+x)*sqrt(x^8-2*x^6-x^4-2*x^2+1+O(x^40)))/(2*x*(x^2+x-1))) \\ Andrew Howroyd, Dec 20 2019 CROSSREFS Cf. A004148, which counts Dyck paths (excursions) avoiding the same consecutive steps. Sequence in context: A107293 A329693 A329976 * A001611 A214448 A039829 Adjacent sequences: A329700 A329701 A329702 * A329704 A329705 A329706 KEYWORD nonn,walk AUTHOR Valerie Roitner, Dec 16 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 31 17:33 EDT 2023. Contains 361668 sequences. (Running on oeis4.)