A125295 Number of different non-self-crossing ways of moving a tower of Hanoi from one peg onto another peg.

1, 2, 12, 1872, 6563711232, 282779810171805015122254036992, 22612323802416302740572466532905158028496454353087246911545156210129751385945830223511552

Offset

0,2

Comments

In other words, a sequence of moves starting with all disks on the starting peg, ending with all disks on the destination peg and never more than once producing the same distribution of disks among the pegs (assuming 3 pegs).

Links

Table of n, a(n) for n=0..6.

Wikipedia, Tower of Hanoi

Index entries for sequences related to Towers of Hanoi

Formula

a(n+1) = (a(n)^2)*(a(n)+1).

a(n) ~ c^(3^n), where c = 1.321902354497090972160055360813404141485787154023407081... . Vaclav Kotesovec, Mar 11 2016

Maple

f:= proc(n) option remember; if n = 0 then 1 else f(n-1)^2*(f(n-1)+1); fi; end; seq(f(n), n=0..7);

Mathematica

t={1, 2}; Do[AppendTo[t, t[[-1]]^3+t[[-1]]^2], {n, 6}]; t (* Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
RecurrenceTable[{a[n+1] == a[n]^2 * (a[n]+1), a[0]==1}, a, {n, 0, 7}] (* Vaclav Kotesovec, Mar 11 2016 *)

Prog

(Scheme)
(define (next n) (* n n (+ n 1)))
(define (list-elements nr-of-elements n0 next)
  (let list-elements ((i 0) (n n0))
    (show i n)
    (let ((i (add1 i)))
      (if (< i nr-of-elements) (list-elements i (next n))))))
(define (show i n) (printf "N(~a)=~a~n~n" i n))
(list-elements 6 1 next)

Crossrefs

Sequence in context: A085912 A085895 A090904 * A222065 A253788 A252738

Adjacent sequences: A125292 A125293 A125294 * A125296 A125297 A125298

Keyword

nonn

Author

Jos Koot, Dec 08 2006

Extensions

Checked by N. J. A. Sloane, Feb 10 2007. The next term is too large to include.

Status

approved