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 A158466 Numerators of EH(n), the expected value of the height of a probabilistic skip list with n elements and p=1/2. 3
 0, 2, 8, 22, 368, 2470, 7880, 150266, 13315424, 2350261538, 1777792792, 340013628538, 203832594062416, 131294440969788022, 822860039794822168, 177175812995012739374, 231553634961214157747264, 1813465925343969651214825522, 14983458468103810854318443432 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A probabilistic skip list is a data structure for sorted elements with O(log n) average time complexity for most operations. The probability p is a fixed internal parameter of the skip list. n fair coins are flipped in a single toss. Those that show tails are collected and reflipped in another single toss. The process is repeated until all the coins show heads. H(n) is the discrete random variable that denotes the number of tosses required. P(H(n)<= k) = (1-(1/2)^k)^n. - Geoffrey Critzer, Dec 13 2009 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..100 P. V. Poblete, J. I. Munro and T. Papadakis, The binomial transform and the analysis of skip lists, Theor. Comput. Sci. 352, 1 (Mar. 2006), 136-158. William Pugh, Skip lists: a probabilistic alternative to balanced trees, Communications of the ACM, v.33 n.6, 668-676, June 1990 Wikipedia, Skip list FORMULA EH(n) = Sum_{k>0} k * ((1-(1/2)^k)^n - (1-(1/2)^(k-1))^n). EH(n) = -Sum_{k=1..n} (-1)^k * C(n,k) / (1-(1/2)^k). EXAMPLE 0, 2, 8/3, 22/7, 368/105, 2470/651, 7880/1953, 150266/35433, 13315424/3011805, 2350261538/513010785, 1777792792/376207909 ... = A158466/A158467 MAPLE EH:= n-> -add((-1)^k *binomial(n, k) /(1-(1/2)^k), k=1..n): seq(numer(EH(n)), n=0..20); MATHEMATICA Table[Sum[x*((1-2^(-x))^n-(1-2^-(x-1))^n), {x, 1, Infinity}], {n, 0, 20}] (* Geoffrey Critzer, Dec 13 2009 *) CROSSREFS Denominators of EH(n): A158467. Cf. A278327. Sequence in context: A238530 A303287 A321068 * A065694 A178129 A203298 Adjacent sequences: A158463 A158464 A158465 * A158467 A158468 A158469 KEYWORD frac,nonn AUTHOR Alois P. Heinz, Mar 19 2009 STATUS approved

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Last modified January 28 23:36 EST 2023. Contains 359905 sequences. (Running on oeis4.)