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;
using System.Globalization;
using System.IO;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        private static void Main(string[] args)
        {
            var n = Scanner.Integer();
            var values = Enumerable.Range(1, n).Select(Check).Select(x => x.ToString());
            OutAllLine(values);
        }

        private static int Check(int val)
        {
            int count = 0;
            for (int x = 1; x <= (int)Math.Sqrt(val); x++)
            {
                for (int y = x; y <= (int)Math.Sqrt(val - x * x); y++)
                {
                    for (int z = y; z <= (int)Math.Sqrt(val - x * x - y * y); z++)
                    {
                        if (x * x + y * y + z * z + x * y + y * z + z * x == val)
                        {
                            if (x == y && y == z)
                            {
                                count += 1;
                            }
                            else if(x == y || y == z || z == x)
                            {
                                count += 3;
                            }
                            else
                            {
                                count += 6;
                            }
                        }
                    }
                }
            }

            return count;
        }

        #region Utility
        static readonly StreamScanner Scanner = new StreamScanner(Console.OpenStandardInput());

        /// <summary> 一括出力 </summary>
        private static void OutAllLine(IEnumerable<dynamic> items)
        {
            var sb = new StringBuilder();
            foreach (var result in items)
            {
                sb.Append(result + "\n");
            }
            sb = sb.Remove(sb.Length - 1, 1);
            Console.WriteLine(sb);
        }

        /// <summary> 素数判定 </summary>
        public static bool IsPrime(int num)
        {
            if (num < 2) {return false;}
            if (num == 2) {return true;}
            if (num % 2 == 0) {return false;}

            double sqrtNum = Math.Sqrt(num);
            for (int i = 3; i <= sqrtNum; i += 2)
            {
                if (num % i == 0) { return false; }
            }
            return true;
        }
        
        public static IEnumerable<int> PrimeFactors(int n)
        {
            int i = 2;
            int tmp = n;

            while (i * i <= n) //※1
            {
                if(tmp % i == 0){
                    tmp /= i;
                    yield return i;
                }else{
                    i++;
                }
            }
            if(tmp != 1) yield return tmp;
        }
        #endregion
    }

    #region Utility Class
    
    public class StreamScanner
    {
        public StreamScanner(Stream stream) { str = stream; }
        private readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }
        private byte read()
        {
            if (isEof) throw new EndOfStreamException();
            if (ptr >= len) {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
        public char Char() 
        {
            byte b = 0;
            do b = read();
            while (b < 33 || 126 < b);
            return (char)b; 
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
                sb.Append(b);
            return sb.ToString();
        }
        public long Long()
        {
            long ret = 0; byte b = 0; var ng = false;
            do b = read();
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-') { ng = true; b = read(); }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                    return ng ? -ret : ret;
                else ret = ret * 10 + b - '0';
            }
        }
        public int Integer() { return (int)Long(); }
        public double Double() { return double.Parse(Scan(), CultureInfo.InvariantCulture); }
        
        /// <summary> 数値読み込み </summary>
        public List<long> ArrayLong(int count = 0)
        {
            var scan = new List<long>();
            for (int i = 0; i < count; i++)
            {
                scan.Add(Long());
            }
            return scan;
        }
        /// <summary> 数値読み込み </summary>
        public List<int> ArrayInt(int count = 0)
        {
            var scan = new List<int>();
            for (int i = 0; i < count; i++)
            {
                scan.Add(Integer());
            }
            return scan;
        }
    }
    public class Mod109
    {
        public const int _7 = 1000000007;
        public const int _9 = 1000000009;
        public const int _3 = 998244353;
        
        private readonly int ModValue;

        public Mod109(int modValue = Mod109._7)
        {
            ModValue = modValue;
        }
        
        /// <summary> 和 </summary>
        public long Addition(IEnumerable<long> nums)
        {
            return nums.Aggregate<long, long>(0, (current, num) => ModifyPositive((current + num) % ModValue));
        }
        
        /// <summary> 差 </summary>
        public long Subtraction(IEnumerable<long> nums)
        {
            return nums.Aggregate<long, long>(0, (current, num) => ModifyPositive((current - num) % ModValue));
        }
        
        /// <summary> 積 </summary>
        public long Multiplication(IEnumerable<long> nums)
        {
            return nums.Aggregate<long, long>(1, (current, num) => ModifyPositive((current * num) % ModValue));
        }

        private long ModifyPositive(long value)
        {
            return value < 0 ? (value + ModValue) : value;
        }
    }
    public class BitArrayMaker
    {
        public List<int> Integer(int bitValue, int length)
        {
            var list = new List<int>();
            for (int i = 0; i < length; i++)
            {
                if (bitValue % 2 == 1)
                {
                    list.Add(i);
                }
                bitValue /= 2;
            }
            return list;
        }
        
        public bool[] Boolean(int bitValue, int length)
        {
            var list = new bool[length];
            for (int i = 0; i < length; i++)
            {
                list[i] = bitValue % 2 == 1;
                bitValue /= 2;
            }
            return list;
        }
    }
    
    #endregion
    
}