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: Time Limit Exceeded)

import java.util.*;

class Main {
	public static void main (String[] args) {
    	Scanner sc = new Scanner(System.in);
      	int N = sc.nextInt();
      	
      	
      	for (int n=1; n<=N; n++) {
          	int c = 0;//counter
        	for (int x=1; x<=Math.sqrt(N); x++) {
            	for (int y=x; y<=Math.sqrt(N); y++) {
                	for (int z=y; z<=Math.sqrt(N); z++) {
                    	if (x*x + y*y + z*z + x*y + y*z + z*x == n) {
                        	if ((x==y)&&(y==z)) {c++;}
                          	else if (x==y) {c+=3;}
                          	else if (y==z) {c+=3;}
                          	else {c+=6;}
                        }
                    }
                }
            }
          	System.out.println(c);
        }
    }
}