Alternating Fibonacci
JavaScript (ES6), 25 bytes

n=&gt;"334130110314"[n%12]-2


0-indexed. You can shorten the string with a slightly recursive version, though it adds 6 bytes:

f=n=&gt;"3341301"[n]-2||f(13-n%12)


This is still shorter than the definitive recursive formula:

f=n=&gt;n&lt;2||f(n-2)+f(n-1)*(-n%2|1)