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.Linq;
using static System.Console;
using static System.Math;

namespace C_AISING2020
{
    class MainClass
    {

        static int[] s;

        public static void Main(string[] args)
        {
            s = Array.ConvertAll(ReadLine().Split().ToArray(), int.Parse);

            int n = s[0];
            var ans = new int[n+1];
            for(int i = 1;i<=100;i++){
                for(int j = 1;j<=100;j++){
                    if(i*i+j*j+i*j>n) continue;
                    for(int k = 1;k<=100;k++){
                        var tmp = i*j+j*k+k*i+i*i+j*j+k*k;
                        if(tmp <=n) ans[tmp]++;
                    }
                }
            }
            for(int i = 1;i<=n;i++){
                WriteLine(ans[i]);
            }
        }

        public static int LowerBound<T>(T[] a, T v)
        {
            return LowerBound(a, v, Comparer<T>.Default);
        }

        public static int LowerBound<T>(T[] a, T v, Comparer<T> cmp)
        {
            var l = 0;
            var r = a.Length - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res == -1) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }
        public static int UpperBound<T>(T[] a, T v)
        {
            return UpperBound(a, v, Comparer<T>.Default);
        }

        public static int UpperBound<T>(T[] a, T v, Comparer<T> cmp)
        {
            var l = 0;
            var r = a.Length - 1;
            while (l <= r)
            {
                var mid = l + (r - l) / 2;
                var res = cmp.Compare(a[mid], v);
                if (res <= 0) l = mid + 1;
                else r = mid - 1;
            }
            return l;
        }
    }
}