Prove that \[\sum_{k=0}^{n}{3n\choose 3k }=\frac{2}{3}\left( 2^{3n-1}+(-1)^n\right). \] The problem was solved by Levi Axelrod and Gerald Marchesi. Their solutions are similar to our in-house solution, which you can see in the following link {{:pow:2026sproblem5.pdf|Solution}}.