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.Scanner;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] res = new int[N + 1];
		for (int x = 1; x <= N; x++) {
			if (x * x > N) {
				break;
			}
			for (int y = 1; y <= x; y++) {
				if (x * x + y * y + x * y > N) {
					break;
				}
				for (int z = 1; z <= y; z++) {
					int tmpRes = x * x + y * y + z * z + x * y + y * z + z * x;
					if (tmpRes > N) {
						break;
					}
					if (tmpRes < N + 1) {
						if (x != y && y != z && z != x) {
							res[tmpRes] += 6;
						} else if (x == y && y == z && z == x) {
							res[tmpRes] += 1;
						} else {
							res[tmpRes] += 3;
						}
					}
				}
			}
		}
		for (int i = 1; i < res.length; i++) {
			System.out.println(res[i]);

		}
	}
}