i) Find the first five terms of the recursively defined sequence ak = 2ak-1 + k for all integers k ≥ 2 with a1 = 1. ii) Find a recurrence for the number tn of ternary words with no consecutive 0s. Then use this recurrence to find t6. iii) Solve the recurrence relation an = 5an-1 - 6an-2 with the initial conditions a0 = 1, a1 = 6. Prove using induction.
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