A007665 Tower of Hanoi with 5 pegs. (Formerly M2414)

1, 3, 5, 7, 11, 15, 19, 23, 27, 31, 39, 47, 55, 63, 71, 79, 87, 95, 103, 111, 127, 143, 159, 175, 191, 207, 223, 239, 255, 271, 287, 303, 319, 335, 351, 383, 415, 447, 479, 511, 543, 575, 607, 639, 671, 703, 735, 767, 799

Offset

1,2

References

A. Brousseau, Tower of Hanoi with more pegs, J. Recreational Math., 8 (1975-1976), 169-176.

Cull, Paul; Ecklund, E. F. On the Towers of Hanoi and generalized Towers of Hanoi problems. Proceedings of the thirteenth Southeastern conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1982). Congr. Numer. 35 (1982), 229--238. MR0725883(85a:68059). - N. J. A. Sloane, Apr 08 2012

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

D. Wood, Towers of Brahma and Hanoi revisited, J. Recreational Math., 14 (1981), 17-24.

Links

Table of n, a(n) for n=1..49.

S. Alejandre, Legend of Towers of Hanoi

J.-P. Allouche, Note on the cyclic towers of Hanoi, Theoret. Comput. Sci., 123 (1994), 3-7.

A. Brousseau, Tower of Hanoi with more pegs, J. Recreational Math 8.3 (1975-6), 169-176. (Annotated scanned copy)

Eric Weisstein's World of Mathematics, Towers of Hanoi

Index entries for sequences related to Towers of Hanoi

Formula

a(n) = - 1 + (1 + A056556(n)*(A056556(n) - 1)/2 + n - A056556(n)*(A056556(n) + 1)*(A056556(n) + 2)/6)*2^A056556(n). - Daniele Parisse, Feb 06 2001

Mathematica

terms = 100;
A056556 = Table[Table[m, {(m+1)(m+2)/2}], {m, 0, (6 terms)^(1/3) // Ceiling}] // Flatten;
a[n_] := With[{t = A056556[[n+1]]}, -1+(1+t(t-1)/2+n-t(t+1)(t+2)/6)*2^t];
Array[a, terms] (* Jean-François Alcover, Feb 28 2019 *)

Prog

(PARI) m=1; n=1; while(n<maxn, for(c=1, (m+1)*(m+2)/2, print1(-1+(1+m*(m-1)/2+n-m*(m+1)*(m+2)/6)*2^m, ", "); n++); m++) \\ K. Spage, Oct 23 2009]

Crossrefs

Cf. A007664. A182058, A056556.

Sequence in context: A122124 A219655 A335039 * A208994 A194602 A337217

Adjacent sequences: A007662 A007663 A007664 * A007666 A007667 A007668

Keyword

nonn

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Status

approved