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

%I A125295 #27 Jan 21 2021 02:53:19
%S A125295 1,2,12,1872,6563711232,282779810171805015122254036992,
%T A125295 22612323802416302740572466532905158028496454353087246911545156210129751385945830223511552
%N A125295 Number of different non-self-crossing ways of moving a tower of Hanoi from one peg onto another peg.
%C A125295 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 A125295 Wikipedia, <a href="http://en.wikipedia.org/wiki/Tower_of_hanoi">Tower of Hanoi </a>
%H A125295 <a href="/index/To#Hanoi">Index entries for sequences related to Towers of Hanoi</a>
%F A125295 a(n+1) = (a(n)^2)*(a(n)+1).
%F A125295 a(n) ~ c^(3^n), where c = 1.321902354497090972160055360813404141485787154023407081... . _Vaclav Kotesovec_, Mar 11 2016
%p A125295 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 A125295 t={1,2};Do[AppendTo[t,t[[-1]]^3+t[[-1]]^2],{n,6}];t (* _Vladimir Joseph Stephan Orlovsky_, Feb 02 2012 *)
%t A125295 RecurrenceTable[{a[n+1] == a[n]^2 * (a[n]+1), a[0]==1}, a, {n, 0, 7}] (* _Vaclav Kotesovec_, Mar 11 2016 *)
%o A125295 (Scheme)
%o A125295 (define (next n) (* n n (+ n 1)))
%o A125295 (define (list-elements nr-of-elements n0 next)
%o A125295   (let list-elements ((i 0) (n n0))
%o A125295     (show i n)
%o A125295     (let ((i (add1 i)))
%o A125295       (if (< i nr-of-elements) (list-elements i (next n))))))
%o A125295 (define (show i n) (printf "N(~a)=~a~n~n" i n))
%o A125295 (list-elements 6 1 next)
%K A125295 nonn
%O A125295 0,2
%A A125295 _Jos Koot_, Dec 08 2006
%E A125295 Checked by _N. J. A. Sloane_, Feb 10 2007. The next term is too large to include.