If you want to do induction on a parameter $a \in \mathbb{Z}$. In the base case, you prove it for $a=0$. And then you suppose it is true for $n$ and prove it for $n+1$ and $n-1$? Is that correct?
Or you have to do induction for all $a\geq 0$ and then for all $a \leq 0$?