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
Examples
The values of f(0), ..., f(3) are 0, 17/3, 424/9, 7889/27.
Links
- 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).
Crossrefs
Cf. A134939.
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
Extensions
Values of f(4) onwards and a general formula found by Max Alekseyev, Feb 02 2008, Feb 04 2008