US-TST 2006 Problem 4

Let $n$ be a positive integer. Find, with proof, the least positive integer $d_{n}$ which cannot be expressed in the form $$\sum_{i=1}^{n}(-1)^{a_{i}}2^{b_{i}},$$ where $a_{i}$ and $b_{i}$ are nonnegative integers for each $i.$