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hop on puyo puyo tetris 2! and help me count polyominoes. submissions may be written in any language.
polyominoes are geometric shapes formed of some number of unit squares put together edge-to-edge. they look like this.
the above are pentaminoes: polyominoes consisting of 5 squares. there are 12 free pentaminoes, 18 if you consider reflections distinct (one-sided), and 63 if you consider reflections and rotations distinct (fixed).
I want to know how many polyominoes there are of any size, not just 5. your challenge, given a non-negative integer, is to compute the number of polyominoes consisting of that number of squares. you may provide a free, one-sided, or fixed count. (or all 3!)
as any language is allowed, there is no fixed API.
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