Polytans are built by connecting rectangular isosceles triangles at their short or long sides called s-sides or h-sides.
Real pieces with a thickness greater than zero can be expanded by putting another triangle on top of them
and this way you get the Stacked Polytans.
The triangle must touch another triangle or square with its whole area and must be aligned to the grid.
In the new layer you can add further triangles as usual.
According to these rules the red pieces are not included, because there are no
matching triangles in the first and second layer.
The green ones are correct examples, because there is a connection between a square
and a triangle and the square is connected with another triangle.
I counted the pieces with a fixed number of triangles and got the following table