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.Scanner;

public class Main {

  public static void main(String[] args) {
    Scanner sc = new Scanner(System.in);
    int N = sc.nextInt();
    int[] ans_array = new int[N + 1];
    int cnt = 0;
    for(int x = 1; x <= 100; x++){
      for(int y = 1; y <= x; y++){
        for(int z = 1; z <= y; z++){
          int tmp = (x * x) + (y * y) + (z * z) + (x * y) + (x * z) + (y * z);
          if(tmp <= N){
            if(x == y && y == z){
              ans_array[tmp]++;
            } else if(x == y || y == z || x == z){
              ans_array[tmp] += 3;
            } else {
              ans_array[tmp] += 6;
            }
          } else {
            break;
          }
        }
      }

    }
    for(int i = 1; i <= N; i++){
      System.out.println(ans_array[i]);
    }
  }
}