15.25. In how many ways can the number $n$ be represented as a sum of positive odd summands? (Representations differing in the order of the summands are considered different.)

## 15.5. Special Recurrence Sequences
15.25. Answer: $F_{n}$. Let the desired number be $x_{n}$. It is clear that $x_{1}=1$ and $x_{2}=1$. We will prove that $x_{n}=x_{n-1}+x_{n-2}$ for $n \geqslant 3$. Indeed, the number of representations with the first term 1 is $x_{n-1}$. If the first term is not less than 3, then 2 can be subtracted from it to obtain a representation of the number $n-2$.