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: Wrong Answer)

import java.io.FileNotFoundException;
import java.util.LinkedHashMap;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) throws FileNotFoundException {

//    	File file = new File("src/in.txt");

        //コード
//    	Scanner sc = new Scanner(file);
    	Scanner sc = new Scanner(System.in);
    	int N = sc.nextInt();
    	int B = (int)Math.pow(N/2, 0.5)+1;
    	LinkedHashMap<Integer, Integer> ans = new LinkedHashMap<Integer,Integer>();
    	for(int x=1;x<=B;x++) {
    		for(int y=1;y<=B;y++) {
    			for(int z=1;z<=B;z++) {
    				int n = x*x+y*y+z*z+x*y+y*z+z*x;
    				if(ans.containsKey(n)) {
    					ans.put(n,ans.get(n)+1);
    				} else {
    					ans.put(n,1);
    				}
    			}
    		}
    	}
    	for(int i=1;i<=N;i++) {
    		if(ans.containsKey(i)) {
        		System.out.println(ans.get(i));
    		} else {
    			System.out.println(0);
    		}

    	}

    }
}