Now I've already done this, so I know what relationship I have to show, but you can figure this sort of thing out by looking at the items in your list if you wanna do this for something else.

Suppose there is a φ^n=F_n*φ+F_(n-1), where F_n is the n'th Fibonacci number.

Okay now what's that? The Fibonacci numbers are numbers starting with F_0=0 and F_1=1, where F_n=F_(n-1)+F_(n-2). Basically, every item on the list past the first is the sum of the previous two. Goes like 0, 1, 1, 2, 3, etc.