Question: A sequence an is defined by the third-order recurrence relation: a n = 5a n 1 8a n 2 + 4a n 3, for n

A sequence an is defined by the third-order recurrence relation:

a_n = 5a_n1 8a_n2 + 4a_n3, for n Z3.

with initial values: a0 = a1 = 1 and a2 = 3.

Derive an explicit closed-form formula for a_n, for all n N.

Define a new sequence bn in terms of a_n, and get a second-order linear homogeneous recurrence relation with constant coefficients for b_n. Solve it, then solve for a_n. Do not use the formula for a 3rd-order recurrence relation.

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