Project Euler Problem 28

问题：

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

答案： 669171001

#include
/*
 * i = 1 , 1
 * i = 3 , 3 5 7 9 q=2
 * i = 5 , 13 17 21 25 q=4
 *  .
 *  .
 *  .
 * i = n , n^2-3*(n-1) n^2-2*(n-1) n^2-(n-1) n^2 q=n-1
 * n = 2k*1, k in [1...500]
 * sum = (16*k^2+4*k+4)_(k 1...500)+1
 *     = 16*kmax*(kmax+1)*(2*kmax+1)/6+4*kmax*(kmax+1)/2+4*kmax+1
 */

int main(void)
{
    int i = 500;
    long sum = 0L;

    sum = 8*i*(i+1)*(2*i+1)/3 + 2*i*(i+1) + 4*i +1;
    printf("%li\n", sum);
    return 0;
}