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.io.PrintWriter;
import java.util.Scanner;

// Aising2020_C
public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();

		PrintWriter out = new PrintWriter(System.out);

		int x = 1;
		int y = 1;
		int z = 1;

		for (int n = 1; n <= N; n++) {
			int fn = 0;
			int count = 0;
			int sqrt = (int) Math.sqrt(n);
			boolean xbreak = false;

			for (int i = 1; i <= sqrt; i++) {
				x = i;
				if (xbreak) {
					break;
				}
				for (int j = 1; j <= sqrt; j++) {
					y = j;
					if (y > z) {
						xbreak = true;
						break;
					}
					for (int k = 1; k <= sqrt; k++) {
						z = k;
						fn = x * x + y * y + z * z + x * y + y * z + z * x;

						if (fn == n && x <= y && y <= z) {
							sqrt = z;
							count += calculateCombination(x, y, z);
						}
					}
				}
			}
			out.println(count);
		}

		sc.close();
		out.flush();
	}

	private static int calculateCombination(int x, int y, int z) {

		if (x == y && y == z && z == x) {
			return 1;
		}

		if (x != y && y != z && z != x) {
			return 6;
		}

		return 3;
	}

}