Tri Tiling - Small Cases

For $n = 2$, there are exactly $3$ ways: all horizontal in each row, two vertical pairs, or a mix. For $n = 4$, you get $11$ ways. These numbers hint at a pattern.

Notice that $n$ must be even. With an odd $n$, you have $3n$ cells (odd total), but each domino covers $2$ cells. You can't tile an odd number of cells with dominoes. The sequence $3, 11, 41, 153, \ldots$ 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.