Number of paths

Consider an equilateral triangle of side \(n\) units, which is divided into unit triangles . Let \( f(n)\) be the number of paths from the triangle in the top row to the middle triangle in the bottom row such that adjacent triangles in the path share a common edge and the path never travels from a lower row to higher row or revisit a triangle . Then determine the value of \(f(2025) \).

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