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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#define FastIO ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;
typedef long int li;
typedef long long ll;
typedef long double ld;

int sqr(int n)
{
	return n * n;
}

int main()
{
	FastIO;
	int n, l, ans;
	cin >> n;
	for (int i = 1; i <= n; i++)
	{
		l = sqrt(i);
		set<vector<int>> ust;
		for (int y = 1; y <= l; y++)
		{
			for (int z = y; z <= l; z++)
			{
				int b = y + z;
				int c = sqr(y) + sqr(z) + y * z - i;
				if (sqr(b) >= 4 * c)
				{
					double d = sqrt(sqr(b) - 4 * c);
					double x = ((double)(-b) + d) / 2.0;
					if (ceil(x) == x)
					{
						if (x >= 1 && sqr(x + y) + sqr(y + z) + sqr(x + z) == 2 * i)
						{
							vector<int> v {x, y, z};
							sort(v.begin(), v.end());
							ust.insert(v);
						}
					}
					x = ((double)(-b) - d / 2.0);
					if (ceil(x) == x)
					{
						if (x >= 1 && sqr(x + y) + sqr(y + z) + sqr(x + z) == 2 * i)
						{
							vector<int> v {x, y, z};
							sort(v.begin(), v.end());
							ust.insert(v);
						}
					}
				}
			}
		}
		ans = 0;
		for (auto q: ust)
		{
			int x = q[0], y = q[1], z = q[2];
			if (x == y && y == z)
				ans++;
			else
				ans += 3;
		}
		cout << ans << "\n";
	}
}