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).
Original entry on oeis.org
0, 17, 424, 7889, 131920, 2099537, 32570104, 498191249, 7559339680, 114166849937, 1719485965384, 25855100073809, 388391603257840, 5830958998038737, 87510144649440664, 1313063982494679569, 19699665930299694400, 295528344080575921937, 4433225354293155251944
Offset: 0
Toby Berger (tb6n(AT)virginia.edu), Jan 23 2008
The values of f(0), ..., f(3) are 0, 17/3, 424/9, 7889/27.
- 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).
Values of f(4) onwards and a general formula found by
Max Alekseyev, Feb 02 2008, Feb 04 2008
A007798
Expected number of random moves in Tower of Hanoi problem with n disks starting with a randomly chosen position and ending at a position with all disks on the same peg.
Original entry on oeis.org
0, 0, 2, 18, 116, 660, 3542, 18438, 94376, 478440, 2411882, 12118458, 60769436, 304378620, 1523487422, 7622220078, 38125449296, 190670293200, 953480606162, 4767790451298, 23840114517956, 119204059374180, 596030757224102, 2980185167180118, 14901019979079416
Offset: 0
David G. Poole (dpoole(AT)trentu.ca)
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- 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 (9,-23,15).
- Index entries for sequences related to Towers of Hanoi
-
[(5^n-2*3^n+1)/4: n in [0..25]]; // Vincenzo Librandi, Oct 11 2011
-
seq( (1 -2*3^n +5^n)/4, n=0..25); # G. C. Greubel, Mar 05 2020
-
Table[(1 -2*3^n +5^n)/4, {n,0,25}] (* G. C. Greubel, Mar 05 2020 *)
-
concat([0,0], Vec(-2*x^2/((x-1)*(3*x-1)*(5*x-1)) + O(x^30))) \\ Colin Barker, Sep 17 2014
-
[(1 -2*3^n +5^n)/4 for n in (0..25)] # G. C. Greubel, Mar 05 2020
More precise definition and more terms from
Max Alekseyev, Feb 04 2008
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.
Original entry on oeis.org
0, 4, 146, 3034, 52916, 857824, 13426406, 206324374, 3138660776, 47471139964, 715573119866, 10765074628114, 161759034582236, 2428929817996504, 36456836245518926, 547058495778290254, 8207730761823753296, 123132640134289171444, 1847139704277091999586, 27708446454015214334794, 415638854666404701309956
Offset: 0
Showing 1-3 of 3 results.
Comments