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Recurrence Relationshard
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Solve the fourth-order recurrence an=5an−2−4an−4a_n = 5a_{n-2} - 4a_{n-4}an​=5an−2​−4an−4​ with initial conditions a0=1,a1=0,a2=1,a3=0a_0 = 1, a_1 = 0, a_2 = 1, a_3 = 0a0​=1,a1​=0,a2​=1,a3​=0. What are all characteristic roots?