Find 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=3an−1−2an−2a_n = 3a_{n-1} - 2a_{n-2}an=3an−1−2an−2 with a0=1,a1=3a_0 = 1, a_1 = 3a0=1,a1=3.
A(x)=11−3x+2x2A(x) = \frac{1}{1-3x+2x^2}A(x)=1−3x+2x21
A(x)=11−3x−2x2A(x) = \frac{1}{1-3x-2x^2}A(x)=1−3x−2x21
A(x)=11−3x+2x2A(x) = \frac{1}{1-3x+2x^2}A(x)=1−3x+2x21 is incorrect; it is 11−2x\frac{1}{1-2x}1−2x1
A(x)=11−3x+2x2A(x) = \frac{1}{1-3x+2x^2}A(x)=1−3x+2x21 is incorrect; it is 1+x1−3x+2x2\frac{1+x}{1-3x+2x^2}1−3x+2x21+x