Tiling Problem

How many ways can a \(2 \times 10\) rectangle be filled with \(1 \times 1\) and \(2 \times 1\) tiles?

One such possible tiling is shown below.

Note: Rotations are allowed, so the \(2 \times 1\) tiles can be placed either horizontally or vertically. This problem is intended to be solved with programming.

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