Question about Tiling a 3 X n board Can anybody please help

Question about Tiling a 3 X n board.
Can anybody please help a fellow out. I\'ve searched everywhere. I need the solution and the logic part, I just don\'t get the logic behind this problem.

Solution

Use this recurrence: F (N) = F (N - 1) + F (N - 3) with base case: F (0) = F (1) = F (2) = 1

Here, F (N) represents no of ways of tiling a 3XN grid with 3X1 or 1X3 tiles.

If you place a 3X1 tile, then you just need to solve for F (N - 1). If you place a 1x3 tile, then you can’t place a 3x1 tile under it. Basically, you will have to place a set of three 1x3 tiles together, hence you solve for F (N - 3).

The sum will give the recurrence.