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Recurrence Relationshard
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For the recurrence relation an=4an−1−an−2−6an−3a_n = 4a_{n-1} - a_{n-2} - 6a_{n-3}an​=4an−1​−an−2​−6an−3​, the characteristic equation has roots r=3,2,−1r = 3, 2, -1r=3,2,−1. Given a0=2,a1=8,a2=22a_0 = 2, a_1 = 8, a_2 = 22a0​=2,a1​=8,a2​=22, what is a3a_3a3​?