A sequence a1, a2, a3, . . . is defined recursively by a1 = 2, a2 = 1, a3 = 3 and an =
Chapter 4, Problem 18(choose chapter or problem)
A sequence a1, a2, a3, . . . is defined recursively by a1 = 2, a2 = 1, a3 = 3 and an = an3 + an2 + an1 for n 4. (a) Determine a4, a5 and a6. (b) Suppose that the first three terms of this sequence were defined instead as a1 = 1, a2 = 2, a3 = 3 but the recurrence relation was not changed. In this case, what are a4, a5 and a6? (c) Suppose that the initial values of the original sequence were not changed but the recur- rence relation is given instead by an = an3 +an1 for n 4. What are a4, a5 and a6 in this case?
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