# Lines in regular polygon

Max Alekseyev maxale at gmail.com
Wed Feb 20 03:10:55 CET 2008

```Dear Franklin,

If I got the definition of your sequence correctly, the Euler
characteristics implies that

a(n) = A007569(n) + A007678(n) - 1

Numerically this sequence is:

0, 1, 3, 8, 20, 42, 91, 136, 288, 390, 715, 756, 1508, 1722, 2835,
3088, 4896, 4320, 7923, 8360, 12180, 12782, 17963, 16344, 25600,
26494, 35451, 36456, 47908, 38310, 63395, 64800, 82368, 84082, 105315,
99972, 132756, 135014, 165243

Regards,
Max

On Feb 19, 2008 5:10 PM,  <franktaw at netscape.net> wrote:
> Take n points, in a regular n-gon (i.e., equally spaced on a circle).
> Connect
> each pair of points (with a straight line segment).  Now count line
> segments,
> where a new segment is considered to start wherever two lines meet.
> I get, starting with n=1:
>
> 0,1,3,8,20,42,91,136
>
> I think a(9) = 243, but I'm not very confident of that.
>
> This sequence is not in the OEIS.
>
> Except for n = 2, a(n) is divisible by n.  Dividing by n, we get, from
> n=3:
>
> 1,2,4,7,13,17
>
> which matches A002466, but if my value for n = 9 is correct, it
> diverges
> thereafter.
>
> Can someone calculate more values (and verify these)?
>