Butch Malahide wrote: > >Now I get 2, 7, 21, 61, 180 for the first five values. Doesn't >match anything in the OEIS. I did the work slowly and carefully >(took about an hour and a half), and so I'm reasonably sure my >numbers are correct.
I wrote a program to do the counts.
It's very slow (it was designed for ease of programming, not for speed of execution), but at least it's automatic.
For n = 1, 2, 3, 4, 5, I get the counts
2, 7, 21, 61, 178
so I match your counts until n = 5.
To help identify the cause of the discrepancy, let me ask this:
For n = 5 (5 segments) how many non-homeomorphic _connected_ compactifications did you get which cannot be represented with less than 5 segments? I get 39 such spaces.