Lines in regular polygon

[franktaw at netscape.net]

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)?

Franklin T. Adams-Watters


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