Recursionhard
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The recurrence an=4an14an2a_n = 4a_{n-1} - 4a_{n-2} has characteristic equation (r2)2=0(r-2)^2 = 0 with repeated root r=2r = 2. The general solution is an=(C1+C2n)2na_n = (C_1 + C_2 n) \cdot 2^n. If a0=1a_0 = 1 and a1=4a_1 = 4, what is the closed-form formula?