The Fibonacci series has a long history in mathematics. It has a curious habit of turning up in various places in nature.

The series is defined very simply. The first two members are 1 and 1. Each subsequent member is defined as the sum of the previous two, so the first few terms are:
1 1 2 3 5 8 13 21 34.

Given 3 consecutive Fibonacci numbers, f(n), f(n+1) and f(n+2), the defining relationship between them is f(n+2) = f(n) + f(n+1). See if you can discover another relationship. The equation varies slightly, depending on whether n is even or odd.