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: Accepted)

#include <bits/stdc++.h>
#define itn int
#define REP(i, n) for (ll i = 0; i < n; i++)
#define IREP(i, n) for (ll i = n - 1; i >= 0; i--)
#define FOR(i, a, b) for (ll i = a; i < b + 1; i++)
#define all(v) v.begin(), v.end()
#define SENTINEL 2000000000
#define NIL -1
using namespace std;
typedef long long ll;

const ll MAX = 510000;
const ll INF = 1LL << 60;
const ll MOD = 1000000007;
template <class T>inline bool chmin(T &a, T b){if(a>b){a=b;return true;}return false;}
template <class T>inline bool chmax(T &a, T b){if(a<b){a=b;return true;}return false;}

int func(int x,int y,int z){
    return x*x+y*y+z*z+x*y+y*z+z*x;
}
int main()
{
    int n;
    cin >> n;
    vector<int> ans(n+1,0);
    int max = sqrt(double(n));
    max++;
    for(int i=1;i<=max;i++){
        for(int j=1;j<=max;j++){
            for(int k=1;k<=max;k++){
                if(func(i,j,k)<=n){
                    ans[func(i,j,k)]++;
                }
            }
        }
    }
    REP(i,n){
        int j=i+1;
        cout << ans[j] << endl;
    }
}