Jumpy, Patient Frog Named Sally And A Math Problem About Her Life-V

A frog, namely, Sally, is jumping about the vertices of a triangle, \(ABC\). Each time, she jumps to an adjacent vertex with equal probability. In how many ways can she get from \(A\) to \(A\) in \(132435\) jumps?

Can you generalise for \(n\) jumps as a little bonus?

This problem is a part of my froggy, soggy set.

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