# 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?