--description--

A triomino is a shape consisting of three squares joined via the edges.

There are two basic forms:

If all possible orientations are taken into account there are six:

Any n by m grid for which nxm is divisible by 3 can be tiled with triominoes. If we consider tilings that can be obtained by reflection or rotation from another tiling as different there are 41 ways a 2 by 9 grid can be tiled with triominoes:

In how many ways can a 9 by 12 grid be tiled in this way by triominoes?

--hints--

triominoes() should return 20574308184277972.

assert.strictEqual(triominoes(), 20574308184277972);

--seed--

--seed-contents--

function triominoes() {

  return true;
}

triominoes();

--solutions--

// solution required