Counting Squares

Let us count the number of distinct shapes that can be formed using \(n\) unit squares that are connected side to side. We consider rotations and reflections to be the same shape.

Consider the above image:
If we have 1 square, then it can only form 1 distinct shape.
If we have 2 squares, then it can only form 1 distinct shape.
If we have 3 squares, then it can form 2 distinct shapes.
If we have 4 squares, then they can form 5 distinct shapes. These are the straight line, the L-shape, the T-shape, the S-shape, and the box, which we see in a game of Tetris.

How many distinct shapes can be formed if we have 10 Squares ?

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