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 C# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;

class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());

		List<int> duplicateList = new List<int>();
		duplicateList.Add(0);


		int result;

		for (int i = 1; i <= N; i++)
        {
			result = 0;
			for(int x = 1;x <= i; x++)
            {
				for (int y = 1; y <= i; y++)
                {
					if ((x * x + y * y + x * y) > i) break;

					for (int z = 1; z <= i; z++)
                    {
						if ((x * x + y * y + z * z + x * y + y * z + z * x) > i) break;

						if((x*x + y*y + z*z + x*y + y*z + z*x) == i)
                        {
							if( x == y && y == z)
                            {
								bool flg = false;
								foreach(var j in duplicateList)
                                {
									if(j == x) flg = true;
								}
                                if (!flg)
                                {
									duplicateList.Add(x);
									result++;
								}
                            }
                            else
                            {
								result++;
                            }
                        }
                    }
				}
			}
			Console.WriteLine(result);
		}
	}
}