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!)
 A182901 Number of weighted lattice paths in B(n) having no valleys. The members of B(n) are paths of weight n that start at (0,0), end on but never go below the horizontal axis, and whose steps are of the following four kinds: an (1,0)-step with weight 1, an (1,0)-step with weight 2, a (1,1)-step with weight 2, and a (1,-1)-step with weight 1. The weight of a path is the sum of the weights of its steps. A valley is a (1,-1)-step followed by a (1,1)-step. 1
 1, 1, 2, 4, 8, 17, 36, 78, 171, 379, 848, 1912, 4341, 9915, 22767, 52526, 121698, 283043, 660579, 1546556, 3631261, 8548643, 20174093, 47716388, 113095740, 268575321, 638954183, 1522668500, 3634346039, 8687404327, 20794957839, 49841956726, 119610395745 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)=A182900(n,0). REFERENCES M. Bona and A. Knopfmacher, On the probability that certain compositions have the same number of parts, Ann. Comb., 14 (2010), 291-306. LINKS FORMULA G.f.: g=g(z) satisfies z^4*(1+z)g^2-(1-z-z^2-z^3)g+1=0. EXAMPLE a(3)=4. Indeed, denoting by h (H) the (1,0)-step of weight 1 (2), and U=(1,1), D=(1,-1), the four paths of weight 3 are hhh, hH, Hh, and UD; none of them has a valley. MAPLE eq := z^4*(1+z)*g^2-(1-z-z^2-z^3)*g+1 = 0: g := RootOf(eq, g): gser := series(g, z = 0, 35): seq(coeff(gser, z, n), n = 0 .. 32); CROSSREFS Sequence in context: A275691 A251691 A157904 * A002845 A072925 A002955 Adjacent sequences:  A182898 A182899 A182900 * A182902 A182903 A182904 KEYWORD nonn AUTHOR Emeric Deutsch, Dec 15 2010 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 May 11 03:20 EDT 2021. Contains 343784 sequences. (Running on oeis4.)