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.ArrayList;
import java.util.Scanner;

public class Main{

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        ArrayList<Integer> result = new ArrayList<Integer>();
        int n = sc.nextInt();
        for(int i =1;i <=n;i++ ) {
        	int count = 0;
        	for(int x =1; x*x <i;x++) {
        		for(int y =x; y*y <i;y++) {
        			for(int z =y; z*z <i;z++) {
                		int f =x*x+y*y+z*z+x*y+y*z+z*x;
                		if(f==i) {
                			if((x==y) && (y==z)) {
                				count++;
                    			break;
                			}
                			else {
                				count = count +3;
                    			break;
                			}
     
                		}
                	}
        		}
        	}
        	result.add(count);
        }
        for(int a:result) {
        	System.out.println(a);
        }
    }

}