# A nice generalization

Probability Level 3

$\large \sum_{k=0}^{\left\lfloor \frac{n-b}{3} \right\rfloor} \binom{n}{3k+b}$

Let $n, b \in \mathbb{Z},$ where $n \geq 1$ and $0 \leq b < 3$. Find the closed form of the sum above.

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