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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
    static int N;
    static int[] result;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        N = sc.nextInt();
        result = new int[N+1];
        f(N);

        for(int i = 1; i <= N; i++) {
            System.out.println(result[i]);
        }
    }
    static void f(int n) {

        for(int i = 1; i <= 101; i++) {
            for(int j = 1; j <= 101; j++) {
                for(int k = 1; k <= 101; k++) {
//                    if(i*i + j*j + k*k + i*j + i*k + j*k == n) {
//                        ++result[n];
//                    }
                    n=i*i + j*j + k*k + i*j + i*k + j*k;
                    if(n>N) break;
                    ++result[n];
                }
            }
        }
    }
}