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: Time Limit Exceeded)

import java.util.*;
public class Main{
  public static void main(String[] args){
    Scanner sc =new Scanner(System.in);
    int N =sc.nextInt();
    for(int i=1;i<=N;i++){
      if(i<4){System.out.println(0);}
      else{
      double I =(double)i;
      double T=Math.sqrt(2*I-8);
      double D=Math.sqrt(2*I/3);
      int t =(int)T;
        int d =(int)D;
       long ans =0;
        for(int j=2;j<=d;j++){
        for(int k=j;k<=t;k++){
          int m =Math.max(d,k);
          for(int l=m;l<=t;l++){
            if(j+1<=k+l){
              if(k+1<=j+l){
                if(l+1<=j+k){
            if(j*j+k*k+l*l==2*i){
              ans =ans+3;
              if((j==k)&&(k==l)){ans =ans-2;}
              }}}}}}}
        System.out.println(ans);
      }
    }
  }
}