Number of way that set of point can be colinear

Question

Assume I have $n$ points in a plane. and I want arrange them in the way that for any point at least I can find two other points that are all the three points are collinar.

I want to know how many way we can arrange these point and of course we do not count those which are isomorphic ( same shape ).

• For instance if we have 3 and 4 points we have only 1 way to arrange them ( all of them should be on a line.
• For 5 points we have 4 ways they are : /,X,L and T.

so what about 6,7 and $n$ in general?

Answer 1

It looks like runes:)

There will be lots of ugly combinatorics.

Sorry that it is not an answer.

And how preciesly do you define the isomorphism. You can get another solution by crossing the isolated triplets of points, this way it would be different shape but the same connectivity possibilities...