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.*;
public class Main {
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    
    int n = sc.nextInt();
    
    int cnt = 0;

    for(int i = 1 ; i <= n ; ++i){
      int count = 0;
      
      if(i%6==0){
        
      }
      int a = i/3;
      int b = a%2;
      int c = i%3;
      int d = i/6;
      if(i%6==0 && (d%2==1||i/6==4)){
        count = i/6;
        cnt++;
      }else if(i>=6 && b==1 && c==2){
        
        if(cnt*6<i && i <(cnt+1)*6){
          count = i/6+2;
          
        }else{
          count = i/6+1;
        }
        
      }

      System.out.println(count);
    }
  }
}