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A125295
Number of different non-self-crossing ways of moving a tower of Hanoi from one peg onto another peg.
2
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).
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
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