Algebra Level 3

The Fibonacci sequence is defined by $$F_1 = 1, F_2 = 1$$ and $$F_{n+2} = F_{n+1} + F_{n}$$ for $$n \geq 1$$. Consider the sequence of every 3rd Fibonacci number, i.e. $$G_n = F_{3n}$$. There are constants $$a$$ and $$b$$ such that $G_n = a G_{n - 1} + b G_{n - 2}$ for every integer $$n\geq 2$$. What is $$a + b$$?

This problem is posed by Muhammad A.

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