This is a problem from Feller's book introduction to probability theory and its application, Vol 1, Chap 3 problem 3.
Let $a$ and $b$ be positive, and $-b . Prove the number of paths to the point $(n,c)$ which meet neither the line $x=-b$ nor $x=a$ is given by the series $\tag1 \sum_{k={-\infty}}^{\infty} (N_{n,4k(a+b)+c}-N_{n,4k(a+b)+2a-c})$ where $N_{n,k}$ is the number of paths going from origin to point $(n,k)$ and only finitely many terms in $(1)$ are non-zero.
The hint suggests to use the reflection repeatedly, but why $4k(a+b)+c$ not $2k(a+b)+c$ ? Is this a typo in the problem?