Given A(x)=∑n=0∞anxn=11−2x−3x2A(x) = \sum_{n=0}^{\infty} a_n x^n = \frac{1}{1-2x-3x^2}A(x)=∑n=0∞anxn=1−2x−3x21, find the recurrence relation for ana_nan.
an=2an−1+3an−2a_n = 2a_{n-1} + 3a_{n-2}an=2an−1+3an−2
an=an−1+an−2a_n = a_{n-1} + a_{n-2}an=an−1+an−2
an=3an−1+2an−2a_n = 3a_{n-1} + 2a_{n-2}an=3an−1+2an−2
an=−2an−1−3an−2a_n = -2a_{n-1} - 3a_{n-2}an=−2an−1−3an−2