login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A005666 Tower of Hanoi with 3 pegs and cyclic moves only (counterclockwise).
(Formerly M1755)
1
0, 2, 7, 21, 59, 163, 447, 1223, 3343, 9135, 24959, 68191, 186303, 508991, 1390591, 3799167, 10379519, 28357375, 77473791, 211662335, 578272255, 1579869183, 4316282879, 11792304127, 32217174015, 88018956287, 240472260607, 656982433791, 1794909388799 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 18.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
J.-P. Allouche, Note on the cyclic towers of Hanoi, Theoret. Comput. Sci., 123 (1994), 3-7.
M. D. Atkinson, The Cyclic Towers of Hanoi, Info. Proc. Letters, 13 (1981), 118-119.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
D. G. Poole, The towers and triangles of Professor Claus (or, Pascal knows Hanoi), Math. Mag., 67 (1994), 323-344.
Amir Sapir, The Tower of Hanoi with Forbidden Moves, The Computer J. 47 (1) (2004) 20, case (ii), cyclic.
FORMULA
a(n) = (1/(4*s3))*((1+s3)^(n+2)-(1-s3)^(n+2))-1 where s3 = sqrt(3).
a(n) = A028859(n) - 1.
G.f.: x*(2+x) / ( (x-1)*(2*x^2+2*x-1) ). - Simon Plouffe in his 1992 dissertation
From Paul Zimmermann, Feb 07 2018: (Start)
a(n) = 2*a(n-1)+2*a(n-2)+3 (same recurrence as A005665).
a(n) = 2*a(n-1)+c(n-1)+2 where c(n) = 2*a(n-1)+1 stands for A005665.
(End)
MATHEMATICA
CoefficientList[Series[z (2 + z)/(z - 1)/(2 z^2 + 2 z - 1), {z, 0, 22}], z] (* Michael De Vlieger, Sep 02 2015 *)
PROG
(Magma) [Floor((1/(4*Sqrt(3)))*((1+Sqrt(3))^(n+2)-(1-Sqrt(3))^(n+2))-1): n in [0..30]]; // Vincenzo Librandi, Sep 03 2015
CROSSREFS
Cf. A005665, A052945 (first differences).
Sequence in context: A018036 A007050 A320811 * A353094 A291411 A159972
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Name clarified by Paul Zimmermann, Feb 09 2018
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 08:07 EDT 2024. Contains 373512 sequences. (Running on oeis4.)