Getting the sequence $\{1, 0, -1, 0, 1, 0, -1, 0, \ldots\}$ without trig? What's the simplest way to write a function that outputs the sequence:

{1, 0, -1, 0, 1, 0, -1, 0, ...}


... without using any trig functions?

I was able to come up with a very complex sequence involving -1 to some complicated formula, but I was hoping there is a more simple solution.

$n$ should start at 0 and go to infinity.

Update:

All the solutions you guys provided are great! I wasn't aware there were so many of them. I should have mentioned that I prefer a solution which doesn't use recursion; imaginary numbers; matrices; functions with if statements; or functions such as ceil, floor, or mod. I'm looking for something using basic algebra: addition/subtraction, multiplication/division, exponents, etc. However, I will accept anything since I didn't  include this clause originally. 

This is what I came up with:

$$a_n=\frac{\left(-1\right)^n+1}{2}\cdot \left(-1\right)^{\left(\frac{n}{2}-\frac{\left(-1\right)^{n+1}+1}{4}\right)}$$

Is there a less complicated way (i.e. fewer terms) to get this same sequence?
Let's try too : $|n \bmod 4-2|-1$
Here is a solution using only 5 bitwise or arithmetic operations:

2 - (((x + 1) | (x + x)) &amp; 3)