[seqfan] A000081 & nonoverlapping circles(?)

[r.shepherd]

Yes, thanks, Jim -- you've convinced me that
1) the A000081 comment is correct,
2) I was counting something else entirely (something harder to
count),
3) *Now*, I understand the parentheses in A000081's comment.

Explanation:  Somehow, I made a couple of incorrect
interpretations of the comment -- and then ran with them when
the first terms, 1, 1, 2, 4, 9, coincided!

Number of configurations in the plane of n equal circles whose
areas do not overlap.  (Tangent circles permitted:  think coins.).

(I consider uniqueness based upon correspondence to unique
graphs with edges connecting centers of tangent circles only --
I think.).

[I don't know/remember much about graphs so help with terminology
would be appreciated.].

Jim, if your offer to look at my .jpg file still holds, I'd like to send
it to you anyway for double-checking before I submit the new
sequence.  (Send me another e-mail if OK).

Thanks,
Rick

From: "Jim Nastos" <nastos at cs.ualberta.ca>
To: "r.shepherd" <r.shepherd at prodigy.net>
Cc: "Sequence Fanatics" <seqfan at ext.jussieu.fr>
Sent: Wednesday, June 11, 2003 5:15 PM


> On Wed, 11 Jun 2003, r.shepherd wrote:
> 
> > Can anyone confirm that this comment in A81 below is correct?
> > Trying to see it for myself I've created a .jpg file that shows
> > 25 arrangements of 5 nonoverlapping circles -- not A000081(6)=20.
> 
>   I haven't drawn out the configurations, but I think I can convince you 
> that 20 is correct:

<convincing argument snipped for now>