A frog sits at one of the vertices of the triangle. She jumps along the vertices of the triangle, moving each time to one

A frog sits at one of the vertices of the triangle. She jumps along the vertices of the triangle, moving each time to one of the neighboring vertices. In how many ways can a frog reach the initial peak in 9 jumps?

The frog initially sits at the point we need. Let us conditionally denote it as a vertex A. Let us denote the number of jumps by X.
X = 9;
Number of vertices = 3;
The frog can jump from one point to two adjacent ones;
We need to raise the number of possible jumps to the 9th power;
Add the number of possible jumps multiplied by -1 to the 9th power [-1];
And divide it all by 3 (the number of vertices);
29 + 2 × (−1) 9 = 510;
510/3 = 170, the number of ways.
Answer: 170.