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%I #27 Jan 21 2021 02:53:19
%S 1,2,12,1872,6563711232,282779810171805015122254036992,
%T 22612323802416302740572466532905158028496454353087246911545156210129751385945830223511552
%N Number of different non-self-crossing ways of moving a tower of Hanoi from one peg onto another peg.
%C 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).
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Tower_of_hanoi">Tower of Hanoi </a>
%H <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F a(n+1) = (a(n)^2)*(a(n)+1).
%F a(n) ~ c^(3^n), where c = 1.321902354497090972160055360813404141485787154023407081... . _Vaclav Kotesovec_, Mar 11 2016
%p 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);
%t t={1,2};Do[AppendTo[t,t[[-1]]^3+t[[-1]]^2],{n,6}];t (* _Vladimir Joseph Stephan Orlovsky_, Feb 02 2012 *)
%t RecurrenceTable[{a[n+1] == a[n]^2 * (a[n]+1), a[0]==1}, a, {n, 0, 7}] (* _Vaclav Kotesovec_, Mar 11 2016 *)
%o (Scheme)
%o (define (next n) (* n n (+ n 1)))
%o (define (list-elements nr-of-elements n0 next)
%o (let list-elements ((i 0) (n n0))
%o (show i n)
%o (let ((i (add1 i)))
%o (if (< i nr-of-elements) (list-elements i (next n))))))
%o (define (show i n) (printf "N(~a)=~a~n~n" i n))
%o (list-elements 6 1 next)
%K nonn
%O 0,2
%A _Jos Koot_, Dec 08 2006
%E Checked by _N. J. A. Sloane_, Feb 10 2007. The next term is too large to include.
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