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A007665
Tower of Hanoi with 5 pegs.
(Formerly M2414)
5
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.
Paul Cull and E. F. Ecklund, 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
Jean-Paul Allouche, Note on the cyclic towers of Hanoi, Theoret. Comput. Sci., 123 (1994), 3-7.
Alfred 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, Tower 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
KEYWORD
nonn
STATUS
approved