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I have this question.

Can we use generating functions to solve the recurrence relation $$\begin{align*} a_1 &= 1,\\ a_2 &= 2,\\ a_n &= a_{n-1} + a_{n-2} \end{align*}$$ Thanks

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    Of course, this is just the Fibonacci sequence with the first few entries (depending on one's exact favorite definition) cut off. Which kind of "solution" are you envisaging here? Something like the $\frac{\phi^n-(\phi-1)^n}{\sqrt 5}$ formula?2012-02-08
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    No, he wants a function whose Taylor expansion contains the terms of the sequence.2012-02-08
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    A harder problem of this type is solved in detail at http://math.stackexchange.com/questions/45111/how-to-solve-this-recurrence-using-generating-functions2012-02-08

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