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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Security.Cryptography.X509Certificates;
using System.ComponentModel.DataAnnotations;
using System.Diagnostics;
using System.Reflection.Metadata;

namespace AtCoder
{
    class Program
    {

        const int BiggestMod = 1000000007;

        public static void Main()
        {

            var num = int.Parse(Console.ReadLine());
            var res = new int[num + 1];

            for (int i = 1; i <= num; i++)
                res[i] = 0;

            for (int i = 1; (i * i + 2 * i) < num; i++)
            {

                for (int j = i; (i * i + j * j + i * j + i + j) < 10000; j++)
                    for (int k = j; k < 10000; k++)
                    {

                        var buf = i * i + j * j + k * k + i * j + j * k + k * i;
                        if (buf > num) break;
                        else
                        {

                            if (i == k) res[buf]++;
                            else if (i == j || j == k) res[buf] += 3;
                            else res[buf] += 6;

                        }


                    }

            }

            for (int i = 1; i <= num; i++)
                Console.WriteLine(res[i]);

        }
    }

}