Find the generating function A(x)A(x)A(x) for an=2an−1+3na_n = 2a_{n-1} + 3^nan=2an−1+3n with a0=0a_0 = 0a0=0.
A(x)=3x(1−2x)(1−3x)A(x) = \frac{3x}{(1-2x)(1-3x)}A(x)=(1−2x)(1−3x)3x
A(x)=x(1−2x)(1−3x)A(x) = \frac{x}{(1-2x)(1-3x)}A(x)=(1−2x)(1−3x)x
A(x)=1(1−2x)(1−3x)A(x) = \frac{1}{(1-2x)(1-3x)}A(x)=(1−2x)(1−3x)1
A(x)=3x1−5x+6x2A(x) = \frac{3x}{1-5x+6x^2}A(x)=1−5x+6x23x