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
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[0]==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
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.
STATUS
approved