This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A247471 Number of paths in B(n) that start with a u step and end with a d step. 0
 0, 0, 0, 1, 1, 2, 5, 11, 26, 62, 148, 356, 860, 2085, 5073, 12382, 30309, 74391, 183042, 451427, 1115741, 2763228, 6856327, 17042633, 42433166, 105816857, 264268595, 660908408, 1655040445, 4149700172, 10416866219, 26178412875, 65858360172, 165850637772 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS B(n) is the set of lattice paths of weight n that start in (0,0), end on the horizontal axis and never go below this axis, whose steps are of the following four kinds: h = (1,0) of weight 1, H = (1,0) of weight 2,  u =  (1,1) of weight 2, and d =  (1,-1)  of weight 1. The weight of a path is the sum of the weights of its steps. LINKS M. Bona and A. Knopfmacher, On the probability that certain compositions have the same number of parts, Ann. Comb., 14 (2010), 291-306. FORMULA G.f.: G = (g - f)/f^2, where g = 1 + z*g + z^2*g + z^3*g^2 and f = 1/(1 - z - z^2). G.f.: G = z^3*(1 - z - z^2)*g^2, where g = 1 + z*g + z^2*g + z^3*g^2. - Emeric Deutsch, Oct 12 2014 EXAMPLE a(6) = 5 because we have uhhhd, uhHd, uHhd, uudd, and udud. MAPLE eqg := g = 1+z*g+z^2*g+z^3*g^2: g := RootOf(eqg, g): f := 1/(1-z-z^2): G := (g-f)/f^2: Gser := series(G, z = 0, 43): seq(coeff(Gser, z, n), n = 0 .. 40); CROSSREFS Sequence in context: A182015 A124217 A095981 * A082397 A051286 A192475 Adjacent sequences:  A247468 A247469 A247470 * A247472 A247473 A247474 KEYWORD nonn AUTHOR Emeric Deutsch, Sep 20 2014 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 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)