SPOJ 3410: SAMER08F - Feynman

Problem Statement

Explanation

How many squares a (4x4) square holds? the answer is-

16 (1x1) squares + 4 (2x2) squares, 9 (3x3) squares, 1 (4x4) squares

Meaning, the answer is \(n^2+(n-1)^2+(n-2)^2+...+1^2\) Which is equivalent to,
\(\sum_{i=1}^{n} i^2 = 1^2 + 2^2 + 3^2 +...+ n^2 = \frac{n(n+1)(2n+1)}{6}\)

Solution

#include<stdio.h>
int main()
{
    int n,x;
    while(scanf("%d",&n)&&n!=0)
    {
        x=(n*(n+1)*((2*n)+1))/6;
        printf("%d\n",x);
    }
    return 0;
}