Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Consider $n$ points equally spaced around the unit circle, joined by all possible combinations of lines to make a complete graph. Let $g(n)$ be the number of triangles formed in the resulting diagram.

For example, $g(3) = 1$, $g(4) = 8$, $g(5) = 35$, $g(6) = 110$.

What is the general formula for $g(n)$?

You can see my initial progress on this puzzle here.

share|improve this question
add comment

1 Answer 1

up vote 4 down vote accepted

http://oeis.org/A006600

share|improve this answer
    
The function given there is for equally spaced points on a circle, and links there go to explanations and formulas. One link on that OEIS page is to: oeis.org/A005732 for general position points on a circle, and gives the formula C(n+3,6)+C(n+1,5)+C(n,5) surely equivalent to a formula at your relevant blog posting. –  Mitch Harris Dec 30 '10 at 17:23
    
Yep - the difficult part is computing the corrections for multiple intersections. But that OEIS link points to some papers which look like they might clear it up (not sure why I didn't think to check OEIS first...) –  Chris Taylor Dec 30 '10 at 17:28
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.