dp/递归 Tri Tiling

Problem Description：

In how many ways can you tile a 3xn rectangle with 2x1 dominoes? Here is a sample tiling of a 3x12 rectangle.

Input：

Input consists of several test cases followed by a line containing -1. Each test case is a line containing an integer 0 ≤ n ≤ 30.

Output：

For each test case, output one integer number giving the number of possible tilings.
Sample Input：
2
8
12
-1
Sample Output：
3
153
2131

类比上楼梯的dp 我们现在要找到3*n的上一个状态(可以是填满的3*2，除去前面所有情况的填满的3*4，除去前面所有情况的填满的3*6…，除去前面所有情况的填满的3*n)，上个状态必定是3乘一个偶数，这样“上个状态”不重不漏。