Let \(f(n)\) be the number of ways in which one can cover a \(3 \times n\) rectangle with dominoes (rectangles with side length \(1 \times 2\)). Find the sum of the digits of \(f(100)\).

**Explicit examples**

\(f(3)=0\)

\(f(4)=11\)

\(f(10)=571\)

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