Question: Derive the generating function A for a series an if an is defined recursively asan =an1+2an2 anda0 =1,a1 =2. Showthatifweusethe reverse of the recurrence relation,

Derive the generating function A for a series an if an is defined recursively asan =an1+2an2 anda0 =1,a1 =2. Showthatifweusethe reverse of the recurrence relation, i.e. an an1x 2an2x2, terms will cancel to zero except for units. By finding the solution to the generating function, derive a closed formula for the sequence.

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