Gidentify the solution of the recurrence relation an = 6an − 1 – 8an − 2 for n ≥ 2 together with the initial conditions a0 = 4, a1 = 10.

Via the generating function method, let



Then take the recurrence,



multiply everything by and sum over all :



Re-index the sums or add/remove terms as needed in order to be able to express them in terms of :







So the recurrence relation is transformed to





For appropriate values of , we can express the RHS in terms of geometric power series:



which tells us that

The correct answer is 10%

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