Determine the generating function A(x)=∑n=0∞anxnA(x) = \sum_{n=0}^{\infty} a_n x^nA(x)=∑n=0∞anxn for the recurrence an=5an−1−6an−2a_n = 5a_{n-1} - 6a_{n-2}an=5an−1−6an−2 with a0=1,a1=3a_0 = 1, a_1 = 3a0=1,a1=3.
1−2x1−5x+6x2\frac{1-2x}{1-5x+6x^2}1−5x+6x21−2x
11−5x+6x2\frac{1}{1-5x+6x^2}1−5x+6x21
1+3x1−5x+6x2\frac{1+3x}{1-5x+6x^2}1−5x+6x21+3x
3x1−5x+6x2\frac{3x}{1-5x+6x^2}1−5x+6x23x