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.*;
//import java.util.stream.Collectors;

public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		
		int n = Integer.parseInt(sc.next());
		Integer[] a = new Integer[n];
		int cnt6 = 1, cnt17 = 1, cnt11 = 1;
		for(int i=1; i<=n; i++){
			if(i == 6 * cnt6 * cnt6){
				cnt6++;
				System.out.println(1);
			}else if(i == 17 * cnt17 + 6 * (cnt17 - 2) || i == 17){
				cnt17++;
				System.out.println(3);
			}else if(i == 11 + cnt11 * 7 + (cnt11 - 1) * 2){
				cnt11++;
				System.out.println(3);
			}else{
				System.out.println(0);
			}
		}
	}
}