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

%I M2414 #37 Sep 06 2023 21:12:39

%S 1,3,5,7,11,15,19,23,27,31,39,47,55,63,71,79,87,95,103,111,127,143,

%T 159,175,191,207,223,239,255,271,287,303,319,335,351,383,415,447,479,

%U 511,543,575,607,639,671,703,735,767,799

%N Tower of Hanoi with 5 pegs.

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

%D 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

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

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

%H S. Alejandre, <a href="http://www.rialto.k12.ca.us/frisbie/mathfair/hanoilegend.html">Legend of Towers of Hanoi</a>

%H J.-P. Allouche, <a href="http://dx.doi.org/10.1016/0304-3975(94)90064-7">Note on the cyclic towers of Hanoi</a>, Theoret. Comput. Sci., 123 (1994), 3-7.

%H A. Brousseau, <a href="/A007664/a007664.pdf">Tower of Hanoi with more pegs</a>, J. Recreational Math 8.3 (1975-6), 169-176. (Annotated scanned copy)

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TowersofHanoi.html">Towers of Hanoi</a>

%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>

%F 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

%t terms = 100;

%t A056556 = Table[Table[m, {(m+1)(m+2)/2}], {m, 0, (6 terms)^(1/3) // Ceiling}] // Flatten;

%t a[n_] := With[{t = A056556[[n+1]]}, -1+(1+t(t-1)/2+n-t(t+1)(t+2)/6)*2^t];

%t Array[a, terms] (* _Jean-François Alcover_, Feb 28 2019 *)

%o (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]

%Y Cf. A007664. A182058, A056556.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)