A134940 Define f(n) by e(n+1) = e(n) + 3^{n+1} - 1 + 2*f(n), where the rational numbers e(n) are defined in A134939; then a(n) is the numerator of f(n).

0, 17, 424, 7889, 131920, 2099537, 32570104, 498191249, 7559339680, 114166849937, 1719485965384, 25855100073809, 388391603257840, 5830958998038737, 87510144649440664, 1313063982494679569, 19699665930299694400, 295528344080575921937, 4433225354293155251944

Offset

0,2

Links

Table of n, a(n) for n=0..18.

M. A. Alekseyev and T. Berger, Solving the Tower of Hanoi with Random Moves, arXiv:1304.3780 [math.CO], 2013-204; 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

f(n) = (6*3^n-1)*(5^n-3^n)/(2*3^n); a(n) = (6*3^n-1)*(5^n-3^n)/2. - Max Alekseyev, Feb 04 2008

G.f.: x*(135*x^2-120*x+17) / ((3*x-1)*(5*x-1)*(9*x-1)*(15*x-1)). - Colin Barker, Dec 26 2012

Example

The values of f(0), ..., f(3) are 0, 17/3, 424/9, 7889/27.

Crossrefs

Cf. A134939.

Sequence in context: A114357 A142997 A330528 * A196676 A027404 A053114

Adjacent sequences: A134937 A134938 A134939 * A134941 A134942 A134943

Keyword

nonn,frac,easy,changed

Author

Toby Berger (tb6n(AT)virginia.edu), Jan 23 2008

Extensions

Values of f(4) onwards and a general formula found by Max Alekseyev, Feb 02 2008, Feb 04 2008

Status

approved