Random Walk on a Triangular Grid

An equilateral triangle is divided by line segments into $9$ congruent small equilateral triangles, two of which are labeled $P$ and $Q$ as shown in the figure. A ball starts in region $P$. Every second, the ball moves to a region chosen uniformly at random from the regions adjacent to its current region, where two regions are adjacent when they share an edge. Find the probability that the ball is in region $Q$ after $n$ seconds.