MathNet 2008-part-05 — 164 problems (EN–VI) Question 124

Let $n \gt 6$ be a positive integer. Determine the number of ways to walk from $(0,0)$ to $(n, 3)$ using only up and right unit steps such that the path does not meet the lines $y=x$ or $y=x-n+3$ except at the start and at the end.