This is no coincidence — it’s because 89=100-10-1, and the ordinary generating function for the Fibonacci sequence is 1/(1-x-x^2) (if you go to wolfram alpha an

This is no coincidence — it’s because 89=100-10-1, and the ordinary generating function for the Fibonacci sequence is 1/(1-x-x^2) (if you go to wolfram alpha and Taylor expand that expression, you’ll see its coefficients are the Fibonacci numbers).