- #1

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## Main Question or Discussion Point

If I have n dots, how many configurations exist for lines that connect them, including no connections?

For example, if I have 0, or 1 dots I believe this should be 0 since no connections are possible (or perhaps I should consider the single dot as having a single connection to itself?) If I have 2 dots, there would be two possibilities, one connection between the two, and zero connections.

To clarify what I mean, for three dots I counted 8: http://i.imgur.com/EHZLcYe.png

For four dots I counted 65, but I could be wrong as I was drawing them and this is error prone: http://imgur.com/Zw0JM0j

The final possibility used 6 lines.

I tried looking through various possibilities and renditions in OEIS, but nothing popped out.

I'm having trouble coming up with a function that returns such an odd sequence as 0,0,2,8,65. I'm hoping that I goofed, because 0,0,2,8,64 looks a lot more palpable.

Surely this function is known? Or something very similar?

Thank you for your time.

For example, if I have 0, or 1 dots I believe this should be 0 since no connections are possible (or perhaps I should consider the single dot as having a single connection to itself?) If I have 2 dots, there would be two possibilities, one connection between the two, and zero connections.

To clarify what I mean, for three dots I counted 8: http://i.imgur.com/EHZLcYe.png

For four dots I counted 65, but I could be wrong as I was drawing them and this is error prone: http://imgur.com/Zw0JM0j

The final possibility used 6 lines.

I tried looking through various possibilities and renditions in OEIS, but nothing popped out.

I'm having trouble coming up with a function that returns such an odd sequence as 0,0,2,8,65. I'm hoping that I goofed, because 0,0,2,8,64 looks a lot more palpable.

Surely this function is known? Or something very similar?

Thank you for your time.