Question 4
Let $A,B,C,D$ be the 4 squares in the centre of a $4\times4$ grid of squares. These 4 squares form the centre of the grid. A frog can jump from one of the 4 squares in the centre to any square in the grid which shares a side. If the frog jumps out of the centre from a particular square for the first time, that square is called an exit square. Find the number of ways in which the frog can start from $A$ with $A$ being the exit square in $n$ jumps. Give your answer in terms of $n$.