sequences and series - Expression for a 0, -1, 0, 1 pattern?

I'm trying to think of a way to create the sequence 0, -1, 0, 1,... with an expression of the type (-1)^{something * k} for k = 1, 2, 3,....

Any ideas? I've sat over this for too long and I know it's not that hard :/

Answer

$$a(k)=\frac{(-1)^\frac{k}{2}+(-1)^\frac{-k}{2}}{2}$$