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 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;
import java.math.*;
import java.lang.*;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int[] data = new int[n+1];

    int x = 1, y = 1, z = 1;
    int sum = 0;

    for (x = 1; x < n; x++) {
      for (y = x; y < n; y++) {
        for (z = y; z < n; z++) {
          sum = (int)Math.pow(x+y+z,2) - x*y - y*z - z*x;
          if (sum > n) continue;
          if (x == y && y == z && z == x) {
            data[sum]++;
          } else if (x == y || y == z || z == x) {
            data[sum] = 3;
          } else if (x != y && y != z && z != x){
            data[sum] = 6;
          }
        }
      }
    }

    for (int i = 0; i <= n; i++) {
      System.out.println(data[i]);
    }
  }

}