Given an=an−1+2an−2a_n = a_{n-1} + 2a_{n-2}an=an−1+2an−2 with a0=1,a1=1a_0=1, a_1=1a0=1,a1=1. What is the generating function A(x)A(x)A(x)?
11−x−2x2\frac{1}{1-x-2x^2}1−x−2x21
1−x1−x−2x2\frac{1-x}{1-x-2x^2}1−x−2x21−x
1+x1−x−2x2\frac{1+x}{1-x-2x^2}1−x−2x21+x
11+x−2x2\frac{1}{1+x-2x^2}1+x−2x21