recurrence for every third Fibonacci number
Source:
November 16, 2009
Problem Statement
The Fibonacci numbers are defined recursively by the equation
F_n \equal{} F_{n \minus{} 1} \plus{} F_{n \minus{} 2}
for every integer , with initial values F_0 \equal{} 0 and F_1 \equal{} 1. Let G_n \equal{} F_{3n} be every third Fibonacci number. There are constants and such that every integer satisfies
G_n \equal{} a G_{n \minus{} 1} \plus{} b G_{n \minus{} 2}.
Compute the ordered pair .