Given the recurrence an=5an−1−6an−2a_n = 5a_{n-1} - 6a_{n-2}an=5an−1−6an−2 with a0=0a_0 = 0a0=0 and a1=1a_1 = 1a1=1, find the closed-form expression for ana_nan.
an=3n−2n−1a_n = 3^n - 2^{n-1}an=3n−2n−1
an=2n−3na_n = 2^n - 3^nan=2n−3n
an=12(3n−2n)a_n = \frac{1}{2}(3^n - 2^n)an=21(3n−2n)
an=3n−2na_n = 3^n - 2^nan=3n−2n