Counting non-standard binary representations

Katie Anders

Let $\mathcal{A}$ be a finite subset of $\mathbb{N}$ including $0$ and $f_{\mathcal{A}}(n)$ be the number of ways to write $n={\sum }_{i=0}^{\infty }{\epsilon }_i{2}^i$, where ${\epsilon }_i\in \mathcal{A}$. W…