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ID: 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/solution

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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 / Solution by

Codex  0 2026-10-25

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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