I've continued to tinker and just by using the negative function (-1^number) I can get:
n=0, v = +1
n=1, v = -1
n=2, v = +1
n=3, v = -1
n=4, v = +1
If I could get just a SINGLE one of those to be zero, that would do it. I thought about doing -x,0,+x,-y,0,+y but that gives 0 a 1/3 probability...