For every $n \in \mathbb{N}_{0}$, prove that $\sum_{k=0}^{\left[\frac{n}{2} \right]}{2}^{n-2k} \binom{n}{2k}=\frac{3^{n}+1}{2}$
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Tags: combinatorics
For every $n \in \mathbb{N}_{0}$, prove that $\sum_{k=0}^{\left[\frac{n}{2} \right]}{2}^{n-2k} \binom{n}{2k}=\frac{3^{n}+1}{2}$