[seqfan] Re: Number of arrangements of n lines in the plane, A241600

[Jon Wild]

On Fri, 16 May 2014, Neil Sloane wrote:

> Several variations are possible:
>
> - allow circles to meet tangentially but without multiple intersection
> points (begins 1, 5, ...)

the next two terms are 27 and 1138.

> - again use circles, but allow multiple intersection points (also begins 1,
> 5, ...).

The next term is 35 (36, if mirror-flipped configurations are allowed to 
be distinct from each other)


> - use ellipses rather than circles.

I have at least 30 new ones for n=3 using ellipses (and no tangencies or 
multiple intersections) - I might have missed some though!

I have some nice pictures for these variations (as well as some others), 
in a document whose beginning I've just posted here:

http://www.music.mcgill.ca/~wild/circleStuff.pdf

The relevant pages for the variations Neil suggested are:

44-48 (tangencies)
50-52 (multiple intersections)
53-55 (ellipses)

(As you can see I went a bit circle mad!)

The rest of that document, which I haven't posted, consisted of my notes 
on how to automate the counting. If anyone wants to work on this I can 
send them what I have, but I won't have much time to pitch in over the 
next few months.

Jon