For , there are exactly ways: all horizontal in each row, two vertical pairs, or a mix. For , you get ways. These numbers hint at a pattern.
Notice that must be even. With an odd , you have cells (odd total), but each domino covers cells. You can't tile an odd number of cells with dominoes. The sequence follows a pattern where each term depends on previous terms. Can you see it? Each new term relates to previous terms in a specific way.