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>
using namespace std;
#define int long long
#define IOS ios_base::sync_with_stdio(0);cin.tie(0)
#define infinite 9123456789
#define PRECISION cout.precision(3); cout.setf(ios::fixed);

int n, f[100000], f1[100000], f2[100000];

void solve(){
	cin >> n;
	int a, b, c;
	for(int i=1; i<=141; i++){
		for(int j=1; j<=141; j++){
			for(int k=1; k<=141; k++){
				if(i*i+j*j+k*k+i*j+j*k+k*i<=n){
					int vez=i*i+j*j+k*k+i*j+j*k+k*i;
					f[vez]++;
				}
			}
		}
	}
	for(int i=1; i<=141; i++){
		for(int j=1; j<=141; j++){
			int k=i;
			if(i*i+j*j+k*k+i*j+j*k+k*i<=n){
				int vez=i*i+j*j+k*k+i*j+j*k+k*i; f1[vez]++;
			}
		}
	}
	for(int i=1; i<=141; i++){
		if(3*i*i<=2*n){
			int vez=6*i*i;
			f2[vez]++;
		}
	}
	for(int i=1; i<=n; i++){
		cout << f[i] << "\n";
	}
}
signed main(){
	solve();
}