This is likely a very easy counting question inspired by some elementary geometry:
Consider a simple rectilinear polygon embedded in a plane in such a way that each of its edges is parallel to one of the coordinate axis. Two such polygons are considered distinct if they are not related by some composition of translation, scalar multiplication and squeeze mapping.
I would like to asses the number of such distinct simple rectilinear polygons which have $2n$ horizontal (equivalently vertical) edges for any chosen $n\in\mathbb N$.
Thank you.