%I A125295
%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>
%F A125295 a(n+1)=(a(n)^2)(a(n)+1)
%F A125295 log a(n) grows somewhat faster than O(3^n).
%p A125295 f:=proc(n) option remember; if n = 0 then 1 else f(n-1)^2*(f(n-1)+1); 
               fi; end;
%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)
%Y A125295 Sequence in context: A085912 A085895 A090904 this_sequence A050649 A003042 
               A000887
%Y A125295 Adjacent sequences: A125292 A125293 A125294 this_sequence A125296 A125297 
               A125298
%K A125295 nonn
%O A125295 0,2
%A A125295 Jos Koot (jos.koot(AT)telefonica.net), Dec 08 2006
%E A125295 Checked by N. J. A. Sloane (njas(AT)research.att.com), Feb 10 2007. The 
               next term is too large to include.