Determine the generating function A(x)=∑n=0∞anxnA(x) = \sum_{n=0}^{\infty} a_n x^nA(x)=∑n=0∞anxn for the sequence satisfying an+2−5an+1+6an=0a_{n+2} - 5a_{n+1} + 6a_n = 0an+2−5an+1+6an=0 with a0=1,a1=2a_0=1, a_1=2a0=1,a1=2.
A(x)=1−3x1−5x+6x2A(x) = \frac{1-3x}{1-5x+6x^2}A(x)=1−5x+6x21−3x
A(x)=1−2x1−5x+6x2A(x) = \frac{1-2x}{1-5x+6x^2}A(x)=1−5x+6x21−2x
A(x)=11−5x+6x2A(x) = \frac{1}{1-5x+6x^2}A(x)=1−5x+6x21
A(x)=1+x1−5x+6x2A(x) = \frac{1+x}{1-5x+6x^2}A(x)=1−5x+6x21+x