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!)
 A325927 Number of Motzkin meanders of length n with an odd number of humps and an odd number of peaks. 4
 0, 0, 1, 4, 13, 38, 105, 280, 737, 1942, 5183, 14100, 39151, 110642, 316751, 914248, 2650655, 7701562, 22400559, 65203428, 189970159, 554165922, 1619018259, 4737859512, 13887657307, 40769959314, 119849273449, 352716050428, 1039027117929 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS A Motzkin meander is a lattice path with steps from the set {D=-1, H=0, U=1} that starts at (0,0), and never goes below the x-axis. A peak is an occurrence of the pattern UD. A hump is an occurrence of the pattern UHH...HD (the number of Hs in the pattern is not fixed, and can be 0). LINKS Andrei Asinowski, Axel Bacher, Cyril Banderier, Bernhard Gittenberger, Analytic combinatorics of lattice paths with forbidden patterns, the vectorial kernel method, and generating functions for pushdown automata, Algorithmica (2019). FORMULA G.f.: ( sqrt((1+t)/(1-3*t)) - sqrt((1+t+2*t^2)/((1-2*t)*(1-t))) - sqrt((1+t^2)/(1-4*t+5*t^2)) + sqrt((1-t^2+2*t^3)/((1-2*t)*(1-t^2-2*t))) ) / (8*t). EXAMPLE For n=3, the a(3)=4 paths are UDH, UDU, UUD, HUD (1 hump, 1 peak). PROG (PARI) seq(n)={my(t='x + O('x*'x^n)); Vec(( sqrt((1+t)/(1-3*t)) - sqrt((1+t+2*t^2)/((1-2*t)*(1-t))) - sqrt((1+t^2)/(1-4*t+5*t^2)) + sqrt((1-t^2+2*t^3)/((1-2*t)*(1-t^2-2*t))) ) / (8*t), -n)} \\ Andrew Howroyd, Aug 12 2019 CROSSREFS Motzkin meanders and excursions with parity restrictions on the number of humps and peaks: A325921: Meanders, #humps=EVEN, #peaks=EVEN. A325922: Excursions, #humps=EVEN, #peaks=EVEN. A325923: Meanders, #humps=ODD, #peaks=EVEN. A325924: Excursions, #humps=ODD, #peaks=EVEN. A325925: Meanders, #humps=EVEN, #peaks=ODD. A325926: Excursions, #humps=EVEN, #peaks=ODD. A325927  (this sequence): Meanders, #humps=ODD, #peaks=ODD. A325928: Excursions, #humps=ODD, #peaks=ODD. Sequence in context: A049611 A084851 A094706 * A056014 A247287 A159036 Adjacent sequences:  A325924 A325925 A325926 * A325928 A325929 A325930 KEYWORD nonn AUTHOR Andrei Asinowski, Aug 10 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 June 13 09:02 EDT 2021. Contains 344981 sequences. (Running on oeis4.)