（Problem 15）Lattice paths

Starting in the top left corner of a 22 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.

How many such routes are there through a 2020 grid?

题目大意：

从一个22网格的左上角开始，有6条（不允许往回走）通往右下角的路。

对于2020的网格，这样的路有多少条？

// （Problem 15）Lattice paths
// Completed on Tue, 11 Feb 2014, 23:58
// Language: VC++2010
//
// 版权所有（C）acutus   (mail: acutus@126.com) 
// 博客地址：http://www.cnblogs.com/acutus/
#include<iostream>
#include<cmath>
using namespace std;

long long a[21][21];

int main()
{
    int i;
    for(i = 0; i < 21; i++)
    {
        a[0][i] = 1;
        a[i][0] = 1;
    }
    for (i = 1; i < 21; i++)
        for (int j = 1; j < 21; j++)
            a[i][j] = a[i][j-1] + a[i-1][j];
    cout<<a[20][20]<<endl;
    return 0;
}

Answer:

137846528820