Tiling Problem

Given a “2 x n” board and tiles of size “2 x 1”, count the number of ways to tile the given board using the 2 x 1 tiles. A tile can either be placed horizontally i.e., as a 1 x 2 tile or vertically i.e., as 2 x 1 tile.

Input n = 3
Output: 3
Explanation:
We need 3 tiles to tile the board of size  2 x 3. 
We can tile the board using following ways
1) Place all 3 tiles vertically. 
2) Place first tile vertically and remaining 2 tiles horizontally.
3) Place first 2 tiles horizontally and remaining tiles vertically

Input n = 4
Output: 5
Explanation:
For a 2 x 4 board, there are 5 ways
1) All 4 vertical
2) All 4 horizontal
3) First 2 vertical, remaining 2 horizontal
4) First 2 horizontal, remaining 2 vertical
5) Corner 2 vertical, middle 2 horizontal