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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 (list; graph; refs; listen; history; text; internal format)
 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 Wikipedia, Tower 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==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. Indentation of the scheme program corrected by Jos Koot, Mar 10 2016 STATUS approved

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Last modified February 19 19:30 EST 2020. Contains 332047 sequences. (Running on oeis4.)