Hello,

While playing with the first terms of the sequence I noticed that is true for . Using induction it can be shown that it is in fact true for any non-negative integer .

Induction hypothesis for all non-negative integer ,

Let's show : let be a non-negative integer. One has so is true.

Let's assume that there exists a non-negative integer such that is true. Let be a non-negative integer.

This shows and we have, for any non-negative integers and , . In particular, for : . Now, what is ?