So if we want to have a function go positive negative we take $(-1)^n$, if we want it to take positive positive negative negative(like was on stack exchange a few days ago, we take:
$(-1)^\cfrac{(n-1)(n+2)}{2}$
What about positive positive positive negative negative negative: So
$f(n) = \left\{ \begin{align} 1, n= 1,2,3,7,8,9,\dots \\-1,n=4,5,6,10,11,12,\dots \end{align} \right. $
How is this created. I understand that I want it the power to be even,even,even,odd,odd,odd. But I can't seem to pin down how this can be made. Any ideas?
More generally, how do set up any combination of positive and negative?