Muhammad's Tri-onacci subsequence

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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