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.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Linq.Expressions;

namespace Main
{
    class Program
    {
        static void Main(string[] args)
        {
            //ここから
            //int n=Readint();
            //string[] str = Console.ReadLine().Split(' ');

            int n = Readint();
            var ans = new int[n];

            for(int x = 1; x < n; x++)
            {
                if (x * x > n) break;
                for(int y = 1; y < n; y++)
                {
                    if (x * x + y * y + x * y > n) break;
                    for(int z = 1; z < n; z++)
                    {
                        int[] xyz = { x, y, z };
                        int fn = x * x + y * y + z * z + x * y + y * z + z * x;
                        if (fn > n) break;
                        ans[fn - 1]++;
                    }
                }
            }

            for(int i = 0; i < n; i++)
            {
                Cout(ans[i]);
            }



            //ここまで
        }

        static void Cout(string s)
        {
            Console.WriteLine(s);
            return;
        }

        static void Cout(int n)
        {
            Console.WriteLine(n);
            return;
        }

        static void Cout(long n)
        {
            Console.WriteLine(n);
            return;
        }

        static int Readint()
        {
            return int.Parse(Console.ReadLine());
        }

        static int[] ReadArray(int n)
        {
            string[] str = Console.ReadLine().Split(' ');
            int[] a = new int[n];
            for (int i=0; i < n; i++){ a[i] = int.Parse(str[i]); }
            return a;
        }
        static long[] ReadArray(long n)
        {
            string[] str = Console.ReadLine().Split(' ');
           long[] a = new long[n];
            for (long i = 0; i < n; i++) { a[i] = long.Parse(str[i]); }
            return a;
        }

        static long Readlong()
        {
            return long.Parse(Console.ReadLine());
        }

        static int Min(int a, int b)
        {
            if (a < b) return a;
            return b;
        }

        static int Max(int a, int b)
        {
            if (a > b) return a;
            return b;
        }


    }

}