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.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;
using System.Numerics;

namespace alsing2020
{
    class Program
    {
        static void Main(string[] args)
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            if (File.Exists("input.txt"))
            {
                Console.SetIn(new StreamReader("input.txt"));
            }
            solve_alsing2020C();
            Console.Out.Flush();
        }
        public static void solve_alsing2020C()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            for (int i = 1; i <= n; i++)
            {
                int cnt = 0;
                for (int x = 1; x <= 100; x++)
                {
                    for (int y = 1; y <= 100; y++)
                    {
                        if (x * x + y * y > i)
                        {
                            break;
                        }
                        for (int z = 1; z <= 100; z++)
                        {
                            int d = x * x + y * y + z * z + x * y + y * z + z * x;
                            if (d > i)
                            {
                                break;
                            }
                            if (x * x + y * y + z * z + x * y + y * z + z * x == i)
                            {
                                cnt++;
                            }
                        }
                    }
                }
                Console.WriteLine(cnt);
            }
        }

        public static void solve_alsing2020B()
        {
            int n = Convert.ToInt32(Console.ReadLine());
            int[] a = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int cnt = 0;
            for (int i = 0; i < n; i++)
            {
                if ((i + 1) % 2 != 0 && a[i] % 2 != 0)
                {
                    cnt++;
                }
            }
            Console.WriteLine(cnt);
        }

        public static void solve_alsing2020A()
        {
            int[] lrd = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int cnt = 0;
            for (int i = lrd[0]; i <= lrd[1]; i++)
            {
                if (i % lrd[2] == 0)
                {
                    cnt++;
                }
            }
            Console.WriteLine(cnt);
        }
    }
}