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# 4.3: Generating Functions and Recurrence Relations

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Recall that a recurrence relation for a sequence $$a_{n}$$ expresses $$a_{n}$$ in terms of values $$a_{i}$$ for $$i < n$$. For example, the equation $$a_{i} = 3a_{i}−1+2^{i}$$ is a first order linear constant coefficient recurrence.

### 4.3.1 How Generating Functions are Relevant

Algebraic manipulations with generating functions can sometimes reveal the
solutions to a recurrence relation.