OFFSET
0,2
COMMENTS
The expected number of random moves is given by a(n)/3^n = a(n)/A000244(n).
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).
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
PROG
(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
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Max Alekseyev, Sep 08 2014
STATUS
approved