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A007665 Tower of Hanoi with 5 pegs.

%I A007665 M2414 #42 Feb 16 2025 08:32:31
%S A007665 1,3,5,7,11,15,19,23,27,31,39,47,55,63,71,79,87,95,103,111,127,143,
%T A007665 159,175,191,207,223,239,255,271,287,303,319,335,351,383,415,447,479,
%U A007665 511,543,575,607,639,671,703,735,767,799
%N A007665 Tower of Hanoi with 5 pegs.
%D A007665 A. Brousseau, Tower of Hanoi with more pegs, J. Recreational Math., 8 (1975-1976), 169-176.
%D A007665 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 A007665 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A007665 D. Wood, Towers of Brahma and Hanoi revisited, J. Recreational Math., 14 (1981), 17-24.
%H A007665 S. Alejandre, <a href="http://www.rialto.k12.ca.us/frisbie/mathfair/hanoilegend.html">Legend of Towers of Hanoi</a>
%H A007665 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 A007665 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 A007665 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TowersofHanoi.html">Towers of Hanoi</a>
%H A007665 <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F A007665 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 A007665 terms = 100;
%t A007665 A056556 = Table[Table[m, {(m+1)(m+2)/2}], {m, 0, (6 terms)^(1/3) // Ceiling}] // Flatten;
%t A007665 a[n_] := With[{t = A056556[[n+1]]}, -1+(1+t(t-1)/2+n-t(t+1)(t+2)/6)*2^t];
%t A007665 Array[a, terms] (* _Jean-François Alcover_, Feb 28 2019 *)
%o A007665 (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 A007665 Cf. A007664. A182058, A056556.
%K A007665 nonn
%O A007665 1,2
%A A007665 _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_