--description--

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 center at position ($x = 0$, $y = 0$);
• the blocks have $y$-coordinates greater than zero (so the plinth is the unique lowest tile);
• the center 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 <u>not</u> 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?

--hints--

balancedSculptures() should return 15030564.

assert.strictEqual(balancedSculptures(), 15030564);

--seed--

--seed-contents--

function balancedSculptures() {

  return true;
}

balancedSculptures();

--solutions--

// solution required