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

        for(int n = 1; n <= N ; n++){
        int x = 0;
        int y = 0;
        int z = 0;
            for(int i = 1; i < (int)Math.sqrt(n) ; i++){
            for(int j = 1; j <(int) Math.sqrt(n) ; j++){
                for(int k = 1; k <= (int)Math.sqrt(n) ; k++){
                    if(((i*i)+(j*j)+(k*k)+(i*j)+(i*k)+(j*k)) == n){
                        x = i;
                        y = j;
                        z = k;
                        i = j = k = n;
                    }

                  }
             }
        }

         if(x <= 0 || y <= 0 || z <= 0)
            System.out.print(0);
        else
        if(x == y && y == z)
            System.out.print(1);
        else
        if(x==y || y == z || x == z)
            System.out.print(3);
        
        
       // System.out.println(" "+ x + " "+ y + " " + z + "--->"+n);
       
        }
        
    }
}