Suppose that b0, b1, b2, . . . is a sequence defined as follows:


b0 =1, b1 =2, b2 =3, and bk = bk−1 + 4*bk−2 + 5*bk−3 for all integers k ≥ 3.

Prove by mathematical induction that bn ≤ 3n for all integers n ≥ 0.