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 Scala (2.13.1) (judge verdict: Accepted)


import scala.collection.mutable
import scala.io.StdIn
import scala.util.control.Breaks


object Main extends App {
  val maxN = StdIn.readLine().toInt
  def f(x:Int,y:Int,z:Int):Int=x*x + y*y+z*z + x*y+y*z+z*x

  val b1 = new Breaks
  val b2 = new Breaks
  val b3 = new Breaks

  var resultList = mutable.ArrayBuffer.empty[Int]
  for (n <- 1 to maxN) {

    var count = 0


      b1.breakable{for (x1 <- 1 to n) {
        if (f(x1, 1, 1) > n) b1.break()

          b2.breakable {for (x2 <- 1 to x1) {
            if(f(x1,x2,1) > n) b2.break()

              b3.breakable {for (x3 <- 1 to x2) {
                  val value = f(x1,x2,x3)
                  if(value > n) b3.break()
                  if(value == n){

                    val d =Set[Int](x1,x2,x3).size match{
                        case 1 => 1
                        case 2 => 3
                        case 3 => 6
                      }
                    count += d
                  }
                }
              }
            }
          }
        }
      }
    resultList += count
    }

  resultList.foreach(println)


}