Tiling （递推）

In how many ways can you tile a 2xn rectangle by 2x1 or 2x2 tiles?
Here is a sample tiling of a 2x17 rectangle.

Input
Input is a sequence of lines, each line containing an integer number 0 <= n <= 250.
Output
For each line of input, output one integer number in a separate line giving the number of possible tilings of a 2xn rectangle.
Sample Input
2
8
12
100
200
Sample Output
3
171
2731
845100400152152934331135470251
1071292029505993517027974728227441735014801995855195223534251

做法：可转化为
F(n)=F(n-1)+2*F(n-2)
为什么F(n-2)的系数为2呢，因为当我们考虑F(n-1)的时候，即在n位置放置了一个2*1的瓦片，而到n-2时，已经在n-1考虑过了两个2*1的瓦片竖着放的情况，所以不用再考虑一遍了。

大数，直接用java吧，
注意当n=0的时候f(0)=1

import java.math.BigInteger;
import java.util.Scanner;

public class Main {
    static BigInteger[] arr=new BigInteger[260];
    static  BigInteger solve(int a)
    {
        if(arr[a]!=null)return arr[a];
        if(a==0)return new BigInteger("1");
        if(a==2)return new BigInteger("3");
        if(a==1)return new BigInteger("1");

        return arr[a]=solve(a-1).add(solve(a-2).multiply(new BigInteger("2"))); 

    }

    public static void main(String[] args) {
        Scanner scan=new Scanner(System.in);
        while(scan.hasNext())
        {
            int a=scan.nextInt();
            System.out.println(solve(a));
        }
    }
}