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Recurrence Relationsmedium
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For the recurrence an=2an−1+an−2a_n = 2a_{n-1} + a_{n-2}an​=2an−1​+an−2​ with a0=1a_0 = 1a0​=1 and a1=3a_1 = 3a1​=3, find the constants c1c_1c1​ and c2c_2c2​ if the characteristic roots are r1=1+2r_1 = 1 + \sqrt{2}r1​=1+2​ and r2=1−2r_2 = 1 - \sqrt{2}r2​=1−2​.