Domino domination!

Let f(n)f(n) be the number of ways in which one can cover a 3×n3 \times n rectangle with dominoes (rectangles with side length 1×21 \times 2). Find the sum of the digits of f(100)f(100).

Explicit examples

  • f(3)=0f(3)=0

  • f(4)=11f(4)=11

  • f(10)=571f(10)=571

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