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