Problem:
Score : 300 points

Problem Statement

Let f(n) be the number of triples of integers (x,y,z) that satisfy both of the following conditions:

1 \leq x,y,z

x^2 + y^2 + z^2 + xy + yz + zx = n

Given an integer N, find each of f(1),f(2),f(3),\ldots,f(N).

Constraints

All values in input are integers.

1 \leq N \leq 10^4

Input

Input is given from Standard Input in the following format:

N

Output

Print N lines. The i-th line should contain the value f(i).

Sample Input 1

20

Sample Output 1

0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
3
0
0

For n=6, only (1,1,1) satisfies both of the conditions. Thus, f(6) = 1.

For n=11, three triples, (1,1,2), (1,2,1), and (2,1,1), satisfy both of the conditions. Thus, f(6) = 3.

For n=17, three triples, (1,2,2), (2,1,2), and (2,2,1), satisfy both of the conditions. Thus, f(17) = 3.

For n=18, three triples, (1,1,3), (1,3,1), and (3,1,1), satisfy both of the conditions. Thus, f(18) = 3.

Solution in Java (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    
    int n = sc.nextInt();
    
    int cnt = 0;
    
    int[] twelve = {0,0,0,0,0,1,0,0,0,0,3,0,0,0,0,0,3,3,0,0};
    
    for(int i=0; i<n; i++){
      System.out.println(twelve[i]);
      if(i==19)
        break;
    }
    
    if(n<=20)
      return;
    
    int sq = (int)Math.sqrt(n);
    
    for(int c=1; c<=n; c++){
      for(int i=1; i <= sq; i++){
        int ii = c - i*i;
          if(ii - i <= 0)
            break;
        for(int j=i; j<= sq; j++){
          int ij = (ii - j*j - i*j);
          if(ij - i - j <= 0)
            break;
          for(int k=j; k<=sq; k++){
            int ijk = (ij - k*k - i*k - j*k);
            if(0 == ijk) {
              cnt++;
              break;
            }
          }
        }
      }
      System.out.println(cnt);
      cnt = 0;
    }
  }
}