TITLE: Generating function for sequence $a_n = 5\times 7^n - 3\times 4^n$
QUESTION [1 upvotes]: How would you proceed to find the generating function of the following sequence?
$$a_n = 5\times 7^n - 3\times 4^n$$
I have no idea where to start for cases where the index appears as exponent.
Thanks in advance!

REPLY [1 votes]: Hint: The sequence satisfies the recurrence $a_{n+2}=11a_{n+1}-28a_n$.
This comes from expanding $(x-7)(x-4)$.
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