> It's the old Fibonacci sequence.
Yep. One way to see this is as a dynamical system: state \\(x\\) represents adult rabbits, and state \\(y\\) represents newborn / immature rabbits. With a single step of the system, all mature rabbits remain mature; mature rabbits spawn one newborn rabbit each; and any existing newborn rabbits become mature.
Well, this is the story I learned from [The Number Devil](https://en.wikipedia.org/wiki/The_Number_Devil), at any rate.