VN-TST 2005 Problem 2

Given $n$ chairs around a circle which are marked with numbers from 1 to $n$ .There are $k$ , $k \leq 4 \cdot n$ students sitting on those chairs .Two students are called neighbours if there is no student sitting between them. Between two neighbours students ,there are at less 3 chairs. Find the number of choices of $k$ chairs so that $k$ students can sit on those and the condition is satisfied.