Sometimes it's difficult even *to write an answer* to a discrete math problem without
an integral or two.

**Example.** The number of integer lattice points that satisfy the conditions
$$-n\leq x,y,z\leq n,\quad -s\leq x+y+z\leq s$$
for some $n$, $s\in\mathbb N$, is equal to
$$\frac{1}{2\pi}\int\limits_{-\pi}^{\pi}\left(\frac{\sin \frac{2n+1}{2}t}{\sin\frac {t}{2}}\right)^3\frac{\sin \frac{2s+1}{2}t}{\sin \frac{t}{2}} dt. $$