Past exam of the year 1 of the computer science course of the University of Oxford / 2019 / Discrete mathematics, continuous mathematics, and probability / 2 / c / i

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- Solution i

Solution

Adding the Fibonacci recurrence and the identical recurrence relation for the Lucas numbers gives

A_{n + 2} = A_{n + 1} + A_{n}, A_{0} = 2, A_{1} = 2.

Linearity preserves this linear recurrence relation; the initial values come from

0 + 2

and

1 + 1

.

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