Solve for the generating function A(x)=∑n=0∞anxnA(x) = \sum_{n=0}^{\infty} a_n x^nA(x)=∑n=0∞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.
A(x)=11−5x+6x2A(x) = \frac{1}{1-5x+6x^2}A(x)=1−5x+6x21
A(x)=11−2x−3x2A(x) = \frac{1}{1-2x-3x^2}A(x)=1−2x−3x21
A(x)=11−5xA(x) = \frac{1}{1-5x}A(x)=1−5x1
A(x)=1−5x1−5x+6x2A(x) = \frac{1-5x}{1-5x+6x^2}A(x)=1−5x+6x21−5x