Inspired by Alan Yan

On a cube, Markov the ant sits at a vertex, \(A\). After every minute, he travels to one of the three adjacent vertices, along an edge, with equal probability. Find the probability that after ten minutes (having traveled exactly ten times) Markov is back at vertex \(A\). Write the answer as \(\dfrac{m}{3^9}\), and enter \(m\).


Inspiration.

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