2011 UNCO Math Contest II Problems/Problem 9

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $T(n)$ be the number of ways of selecting three distinct numbers from $\left\{1, 2, 3,\cdots ,n\right\}$ so that they are the lengths of the sides of a triangle. As an example, $T(5) = 3$; the only possibilities are $\{2-3-4\},\{ 2-4-5\}$, and $\{3-4-5\}$.

(a) Determine a recursion for T(n).

(b) Determine a closed formula for T(n).