How many triangles has a complete graph. Recursive Equation

I need to find the solution with a recursive equation. I found the solution with combinations: $${n}\choose{}3$$

but I don't know how to find it with recursive equations. I don't find a pattern to resolve it

Thanks

Let $$T_n$$ be the number of triangles in a complete graph of size $$n$$ for $$n\geq 3$$. Deduce that $$T_{n+1} = T_n + \binom{n}{2}$$, as it amounts to considering if a triangle is contained in the complete subgraph on $$n$$ vertices or not. With $$T_3=1$$, it follows that $$T_n=1+\sum_{k=3}^{n-1}\binom{k}{2}=1+\sum_{k=3}^{n-1}k(k+1)/2$$. Simplifying this will give you the answer.