What is the generating function A(x)=∑n=0∞anxnA(x) = \sum_{n=0}^{\infty} a_n x^nA(x)=∑n=0∞anxn for the sequence an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2 with a0=0,a1=1a_0=0, a_1=1a0=0,a1=1?
A(x)=11−x−x2A(x) = \frac{1}{1-x-x^2}A(x)=1−x−x21
A(x)=x1−x−x2A(x) = \frac{x}{1-x-x^2}A(x)=1−x−x2x
A(x)=x1+x−x2A(x) = \frac{x}{1+x-x^2}A(x)=1+x−x2x
A(x)=11+x+x2A(x) = \frac{1}{1+x+x^2}A(x)=1+x+x21