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A125295
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Number of different non-self-crossing ways of moving a tower of Hanoi from one peg onto another peg.
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0
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OFFSET
| 0,2
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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).
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LINKS
| Wikipedia, Tower of Hanoi
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FORMULA
| a(n+1)=(a(n)^2)(a(n)+1)
log a(n) grows somewhat faster than O(3^n).
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MAPLE
| f:=proc(n) option remember; if n = 0 then 1 else f(n-1)^2*(f(n-1)+1); fi; end;
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MATHEMATICA
| t={1, 2}; Do[AppendTo[t, t[[-1]]^3+t[[-1]]^2], {n, 6}]; t (* From Vladimir Joseph Stephan Orlovsky, Feb 02 2012 *)
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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)
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CROSSREFS
| Sequence in context: A085912 A085895 A090904 * A050649 A003042 A000887
Adjacent sequences: A125292 A125293 A125294 * A125296 A125297 A125298
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KEYWORD
| nonn
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AUTHOR
| Jos Koot (jos.koot(AT)telefonica.net), Dec 08 2006
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EXTENSIONS
| Checked by N. J. A. Sloane (njas(AT)research.att.com), Feb 10 2007. The next term is too large to include.
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