Ononot — For the non-homogeneous recurrence an = 4a{n-1} - 3a{n-2} +

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Recurrence Relationshard

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For the non-homogeneous recurrence $a_n = 4a_{n-1} - 3a_{n-2} + n^2 + 2,$ the homogeneous characteristic roots are 1 and 3.

Using the method of undetermined coefficients, what form should the particular solution $a_n^{(p)}$ take?