Fr the third order recurrence relation an 3an-1

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Fr the third order recurrence relation an 3an-1 - 3an-2

Compute the answer of the given problem

Problem- For the third order recurrence relation an = 3an-1 - 3an-2 + an-3 where a0 = -2, a1=4, and a2=12, prove that an=n2 + 5n -2 is an explicit solution.

I want help to describe the third order recurrence relation.

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