I assume that you mean integer solutions.
Off the top of my head I don't see how to do this with a single combination because different choices for x lead to different possibilities for y and z, and order seems to matter.
For example, if x = 5, then there are 6 possibilities for the pair (y,z): (-5, 0), (-4, -1), ..., (0,-5)
Similarly, if x = 6, then there are 5 possibilities for the pair (y,z).
Continuing in this fashion, we see that there are 6+5+4+3+2+1=21 possibilities for the triple (x,y,z).