Tiling Problem

How many ways can a 2×102 \times 10 rectangle be filled with 1×11 \times 1 and 2×12 \times 1 tiles?

One such possible tiling is shown below.

Note: Rotations are allowed, so the 2×12 \times 1 tiles can be placed either horizontally or vertically. This problem is intended to be solved with programming.

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