A066313 aperiodic bracelets

[Christian G. Bower]

I just sent a message to Neil that will hopefully clarify the meaning of
A066313.

The fourth message in the discussion worked out the right interpretation.

To make it clearer, I'm suggestion a definition that uses only necklace
and not bracelet, since the structure cannont be turned over as one
can do with a bracelet, it can only be turned over if the colors are
simultaneously flipped.  The actual change I am suggesting has a title

Number of aperiodic necklaces with n red or blue beads such that two necklaces
are equivalent under the operation (turn necklace over and switch the two
colors).

and an example:

The equivalence requires the "turning over" operation and the "switching
colors" operation to be simultaneous; thus rrrbbrrb is equivalent to rbbrrbbb,
but not to bbbrrbbr.

Christian

------ Original Message ------
From: Hugo Pfoertner <all at abouthugo.de>
To: seqfan at ext.jussieu.fr
Subject: A066313 aperiodic bracelets

> Currently there is a discussion in the newsgroup sci.math on
> http://www.research.att.com/~njas/sequences/A066313 
> starting at
> http://groups.google.com/group/sci.math/msg/58f3cd40eeac99d8
> It seems that the current definition of A066313 is at least unclear. Can
> someone experienced in this field take care of the necessary
> corrections?
> 
> Hugo Pfoertner
>