A combinatorial problem on arithmetic progressions

[Santi Spadaro]

Hi everyone! It's a great pleasure for me to partecipate in the 
SeqFan Mailing List. I'm a physics student from Sicily. To be exact I 
live in a village named Pagliara but I study physics at the 
University of Messina.

I would like to begin my contribution to the list with the following 
simple combinatorial problem:

"How many arithmetic progressions of k terms and any mean can be 
extracted from the set of the first n natural numbers?"

I myself had proposed it to me a few years ago, and I resolved it for any k.
The solution for k=3 is the sequence named "Quarter Squares", and for 
k>3 I also found sequences which are in NJA Sloane's Encyclopedia.

I recently submitted a comment on Quarter Squares to NJAS's OEIS 
dealing with it, so I would like to know: has anyone of you ever 
heard of this problem, or a problem similar to it?

Thank you very much, I hope not to have bored you...

Cheers

Santi Spadaro

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