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Solve the recurrence relation a n = 3 a n - 1 - 3 a n - 2 + a n - 3 + 1

Solve the recurrence relation

a_{n} = 3 a_{n - 1} - 3 a_{n - 2} + a_{n - 3} + 1

given the initial conditions

a_{0} = 2,

a_{1} = 2, a_{2} = 4 .

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