Possible Checker Placements

On a 40 by 40 square grid, Victor covers a 1 by 1 square with a checker piece. He is then able to cover the rest of the squares with 533 1×3 1 \times 3 triminos.

What is the total number of squares on which the checker piece could be placed?

Details and assumptions

The 1×3 1 \times 3 trimino consists of 3 squares arranged in a straight row (or column).

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