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

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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