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: Time Limit Exceeded)

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

namespace easy_Atcoder
{
    class Program
    {
        static void Main(string[] args)
        {
            int N = int.Parse(Console.ReadLine());
            int count = 0;
            int rootN = N - (int)Math.Sqrt(N)/3;
            for(int h=1; h <= N; h++){
                count = 0;
                for(int i = 1; i< rootN;i++){
                    for(int j = 1; j<rootN;j++){
                        for(int k = 1; k<rootN;k++){
                            count += Calc(i,j,k,h);
                        }
                    }
                }
                Console.WriteLine(count);
            }
        }
        static int Calc(int x, int y, int z,int n){
            if(x*x+y*y+z*z+x*y+y*z+z*x == n){
                return 1;
            }else{
                return 0;
            }

        }
            // long[] NK = Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
            // long N = NK[0];
            // long K = NK[1];
            // long K = long.Parse(Console.ReadLine());
            // int[] abc = Array.ConvertAll(Console.ReadLine().Split(),int.Parse);
            // string S = Console.ReadLine();
            // int x = int.Parse(Console.ReadLine());
            // int b = int.Parse(Console.ReadLine());
            // int N = int.Parse(Console.ReadLine());
            // float N = float.Parse(Console.ReadLine());
            // string c = Console.ReadLine();
            // string B = Console.ReadLine();
            // string[] s = Console.ReadLine().Split();
            // var s = (new string[] { Console.ReadLine(), Console.ReadLine(), Console.ReadLine() }).Select(float.Parse);
            // float[] a = Array.ConvertAll(Console.ReadLine().Split(),float.Parse);
            // var X = Console.ReadLine();
            // int[,] abcd = new int[NMQ[2],4];
            // int[] A = new int[NMQ[0]];
            // int[] A_num = new int[NMQ[0]];
            // long[] s=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
            // var hs=new Dictionary<long,long>();
            // for(int i=0;i<s[0];i++){
            //     long[] q=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
            //     if(hs.ContainsKey(q[0])){hs[q[0]]+=q[1];}
            //     else{hs.Add(q[0],q[1]);}
            // }
        
        // //最小公倍数
        // static long Lcm(long a, long b)
        // {
        //     return a/Gcd(a,b)*b;
        // }

        // //最大公約数
        // static long Gcd(long m, long n)
        // {
        //     if(n==0)return m;
        //     return Gcd(n,m%n);
        // }
    }
}