Prove that: $ \sum_{i = 0}^k {n \choose i} = \sum_{i = 0}^k {n - 1 - i \choose k - i}2^i $

Question

I've been stuck with problem for quite a while:

Prove that: $$ \sum_{i = 0}^k {n \choose i} = \sum_{i = 0}^k {n - 1 - i \choose k - i}2^i $$ for $k$ in $\{0,\dots,n-1\}$. I would love to get a hint how to solve it using combinatorial interpretation.