Let us define a balanced sculpture of order n as follows:
When counting the sculptures, any arrangements which are simply reflections about the y-axis, are not counted as distinct. For example, the 18 balanced sculptures of order 6 are shown below; note that each pair of mirror images (about the y-axis) is counted as one sculpture:
There are 964 balanced sculptures of order 10 and 360505 of order 15.
How many balanced sculptures are there of order 18?
These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK