Determine the asymptotic growth rate of the sequence ana_nan defined by an=2an−1+an−2−2an−3a_n = 2a_{n-1} + a_{n-2} - 2a_{n-3}an=2an−1+an−2−2an−3 with a0=1,a1=1,a2=2a_0=1, a_1=1, a_2=2a0=1,a1=1,a2=2.
O(n⋅2n)O(n \cdot 2^n)O(n⋅2n)
O(1n)O(1^n)O(1n)
O(n2)O(n^2)O(n2)
O(2n)O(2^n)O(2n)