Problem 275

Balanced Sculptures

Let us define a *balanced sculpture* of order `n` as follows:

- A polyomino made up of
`n`+1 tiles known as the*blocks*(`n`tiles)

and the*plinth*(remaining tile); - the plinth has its centre at position (
`x`= 0,`y`= 0); - the blocks have
`y`-coordinates greater than zero (so the plinth is the unique lowest tile); - the centre of mass of all the blocks, combined, has
`x`-coordinate equal to zero.

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
**