Rubik cube sequence?

[Alex Healy]

Yes, as far as I know the question of the diameter of the Rubik's cube
Cayley graph is still open.  

I do have code that I used to generate the sequences: A060010, A061713.
That code, also spits out the number of states reachable in n moves, so I'll
run it again and submit the results to the EIS (and to the list); just give
me a few hours. ;)  I guess I never submitted them in the first place
because it's a finite sequence . . . I'm glad there's interest though.

Alex

> -----Original Message-----
> From: Brian L. Galebach [mailto:briang at SEGmail.com] 
> Sent: Friday, February 21, 2003 2:21 PM
> To: seqfan at ext.jussieu.fr
> Cc: briang at ProbabilitySports.com
> Subject: RE: Rubik cube sequence?
> 
> 
> Last time I checked (maybe about a year ago) it was still not 
> known what the maximum number of moves was to solve the cube 
> from any possible position. Therefore, the complete sequence 
> would not yet be known.
> 
> Brian
> 
> -----Original Message-----
> From: N. J. A. Sloane [mailto:njas at research.att.com]
> Sent: Friday, February 21, 2003 1:50 PM
> To: seqfan at ext.jussieu.fr
> Subject: Rubik cube sequence?
> 
> 
> Inspired by Jaap Scherphuis's excellent web site
> on generalizations of Rubik's cube,
> i've added several sequences to the OEIS giving the number
> of positions that are n moves away from the start in
> these puzzles.  For example:
> 
> %I A079761
> %S A079761 
> 1,9,54,321,1847,9992,50136,227536,870072,1887748,623800,2644
> %N A079761 Number of positions that are n moves from the 
> starting position in the 2 X 2 X 2 Rubik cube puzzle. %C 
> A079761 A puzzle in the Rubik cube family. The total number 
> of distinct positions is 3674160. A half-turn is considered 
> to be one move. %D A079761 D. R. Hofstadter, Metamagical 
> Themas, Basic Books, NY, 1985, p. 359. %H A079761 Jaap 
> Scherphuis, <a 
> href="http://www.geocities.com/jaapsch/puzzles/">Puzzle 
> Pages</a> %K A079761 nonn,fini,full,new %O A079761 0,2 %A 
> A079761 njas, Feb 20 2003
> 
> Does anyone know the analogous sequence for the 3 X 3 X 3 
> cube, or even the beginning of that sequence?
> 
> NJAS
>