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: Accepted)

import java.util.*;

public class Main {
  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in); 
    int N = sc.nextInt();
    for (int i =1; i<N+1; i++) {
      int count =0;
      for (int x =1; x<Math.sqrt(i); x++) {
        for (int y =x; y<Math.sqrt(i); y++) {
          double z = (-(x+y) + Math.sqrt(4 * i - 3 * x * x - 3 * y * y - 2 * x * y))/2;
          if (z % 1 != 0 || z < y) {
            continue;
          } else {
            if (x == y && y == z && z == x) {
              count++;
            } else if (x == y || y == z) {
              count+=3;
            } else {
              count+=6;
            }
          }
        }
      }
      System.out.println(count);
    }
  }
}