GeneratingFunction US Putnam
Difficult

Problem - 4332

Let $\alpha(n)$ be the number of ways to write a positive integer $n$ as the sum of $1$s and $2$s. Let $\beta(n)$ be the number of ways to write $n$ as a sum of several integers greater than $1$. Different orders are treated as different. Prove $\alpha(n)=\beta(n+2)$.

The solution for this problem is available for $0.99. You can also purchase a pass for all available solutions for$99.