Consider a convex \((n+2)\)-gon. Let \(a_n\)​ denote the number of ways to add non-crossing chords to this polygon, including the case where no chords are added (i.e., \(a_0=a_1=0\) and \(a_2=3\)).

Find a recurrence relation for the sequence \(a_n​\) and determine its generating function.

The best solution was submitted by 김준홍 (수리과학과 석박통합과정, +4). Congratulations!

Here is the best solution of problem 2025-08.

Other solutions were submitted by 김동훈 (수리과학과 22학번, +3), 신민규 (수리과학과 24학번, +3), 정서윤 (수리과학과 학사과정, +3), 채지석 (수리과학과 석박통합과정, +3), Anar Rzayev (수리과학과 19학번, +3).