UVa 11401 - Triangle Counting

11401 - Triangle Counting

 * http://icpcres.ecs.baylor.edu/onlinejudge/index.php?option=com_onlinejudge&Itemid=8&category=26&page=show_problem&problem=2396

Summary
Calculate the number of non-congruent non-degenerate scalene triangles with integer sides with maximum side length n.

Explanation
The number of triangles with longest side $$n$$ is $$f(n) = (n-3) + (n-5) + (n-7) + ...$$ for as long as that sequence remains positive. Notice that, for $$n > 3$$, $$f(n) + f(n-1) = {n-2 \choose 2}$$. From here, find a recurrence relation (or two) for $$F(n) = n \sum_{k=3}^n {f(k)}$$ and solve it to be able to complete the problem within the time limit.

Gotchas

 * The program should terminate for any input value less than 3, but 3 itself needs to be processed.

Implementations

 * Using long long integers is sufficient for the problem.

Input
5 8 3 1000000 2

Output
3 22 0 83332958333750000