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.*;
import java.io.*;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int count = 0;
		int mul = 0;
        for(int i = 1; i <= n; i++) {
			count = 0;
			for(int x = 1; x < 100; x++) {
				if((x * x + x * 2 + 3) > i) {
					System.out.println(count);
					break;
				}
				for(int y = 1; y < 100; y++) {
					for(int z = 1; z < 100; z++) {
						mul = (x * x) + (y * y) + (z * z) + (x * y) + (y * z) + (z * x);
						if(mul == i){
							count++;
						}
						if(mul > i){
							break;
						}
					}
					mul = (x * x) + (y * y) + (x + y) + x + y + 1;
					if(mul > i){
						break;
					}
				}
			}
		}
    }
}