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.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = Integer.parseInt(sc.next());
		sc.close();

		for(int i = 1; i <= N; i++) {
			int n = i;
			int count = 0;
			int tm = (int)Math.floor(n / 2);
			int tmp = (int)Math.floor(Math.sqrt(tm));
			for(int j = 1; j <= tmp; j++) {
				n = i;
				n -= 2 * j * j;
				if(n > 0) {
					double check = Math.sqrt(n);
					if(check == Math.floor(check) && check != 1) {
						if(check - j == j) {
							count += 1;
						}else {
							count += 3;
						}
					}
				}else {
					continue;
				}
			}
			System.out.println(count);
		}
	}

}