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.*;
import java.util.function.*;
import java.math.*;
public class Main {
    public static void main(String[] args){
Scanner s = new Scanner(System.in);
		int N = Integer.valueOf(s.next());
		int[] ret = new int[N+1];
		
		for(int x = 1; x < 100; x++) {
			for(int y = 1; y < 100; y++) {
				for(int z = 1; z < 100; z++) {
					int cur = calc(x, y, z);
					if(cur <= N) {
						ret[cur]++;
					}else {
						break;
					}
				}
			}
		}
		
		for(int i = 1; i <= N; i++) {
			System.out.println(ret[i]);
		}
		
		
	}
	
	private static int calc(int x, int y, int z) {
		return (x*x + y*y + z*z + x*y + y*z + z*x);
	}
}