For the recurrence an=2an−1+an−2+5⋅3na_n = 2a_{n-1} + a_{n-2} + 5 \cdot 3^nan=2an−1+an−2+5⋅3n with a0=0,a1=1a_0 = 0, a_1 = 1a0=0,a1=1, what is the asymptotic form (dominant term) as n→∞n \to \inftyn→∞?
∼(2.41)n\sim (2.41)^n∼(2.41)n
∼3n\sim 3^n∼3n
∼52⋅3n\sim \frac{5}{2} \cdot 3^n∼25⋅3n
∼n⋅3n\sim n \cdot 3^n∼n⋅3n