A246961 Numerator of the expected number of random moves in Tower of Hanoi problem with n disks starting at a randomly chosen valid configuration and ending with all disks at peg 1.
0, 4, 146, 3034, 52916, 857824, 13426406, 206324374, 3138660776, 47471139964, 715573119866, 10765074628114, 161759034582236, 2428929817996504, 36456836245518926, 547058495778290254, 8207730761823753296, 123132640134289171444, 1847139704277091999586, 27708446454015214334794, 415638854666404701309956
Offset: 0
Links
- M. A. Alekseyev and T. Berger, Solving the Tower of Hanoi with Random Moves. In: J. Beineke, J. Rosenhouse (eds.) The Mathematics of Various Entertaining Subjects: Research in Recreational Math, Princeton University Press, 2016, pp. 65-79. ISBN 978-0-691-16403-8
- Index entries for linear recurrences with constant coefficients, signature (32,-342,1440,-2025).
Programs
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PARI
concat(0, Vec(-2*x*(135*x^2-9*x-2)/((3*x-1)*(5*x-1)*(9*x-1)*(15*x-1)) + O(x^100))) \\ Colin Barker, Sep 17 2014
Formula
a(n) = ( (3^n - 1)*(5^(n+1) - 2*3^(n+1)) + 5^n - 3^n ) / 4.
G.f.: -2*x*(135*x^2-9*x-2) / ((3*x-1)*(5*x-1)*(9*x-1)*(15*x-1)). - Colin Barker, Sep 17 2014
Comments