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
Keywords
Links
Programs
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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; seq(f(n), n=0..7);
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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 *) -
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)
Formula
a(n+1) = (a(n)^2)*(a(n)+1).
a(n) ~ c^(3^n), where c = 1.321902354497090972160055360813404141485787154023407081... . Vaclav Kotesovec, Mar 11 2016
Extensions
Checked by N. J. A. Sloane, Feb 10 2007. The next term is too large to include.
Comments