Have a 2xn checkerboard made of 2 kinds of tiles:
- 1x1 square tile
- L-tile, which is a 2x2 square tile with a 1x1 square removed from the corner. This tile can be rotated.
I'm trying to create a recursive formula $t(n)$ to find the number of possible tilings. This is what I have so far:
n=1 t(1) = 1 because can only have 2 1x1 tiles
n=2 t(2) = 5 because you can have:
- All 1x1 tiles (1 option)
- A 1x1 tile and the L-tile rotated 4 different ways (4 options)
n=3 t(3) = 11 because you can have:
0 L-tiles, so all 1x1 tiles (1 option)
1 L-tile which can be rotated 8 ways and the rest filled with 1x1 squares (8 options)
2 L-tiles, which can be rotated 2 ways (2 options)
Is this correct / am I on the right track? I'm not sure how to find the recursive formula this way.