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 Ruby (2.7.1) (judge verdict: Accepted)

class Problem
  attr_accessor :a, :b, :n, :m, :h, :w, :dp

  def initialize
    @n = gets.to_s.to_i
    @a = Array.new(n+1, 0)
  end

  def solve
    rec
    @a
  end

  def rec
    max = (Math.sqrt(n) * 1.3).to_i
    1.upto(max) do |x|
      1.upto(max) do |y|
        1.upto(max) do |z|
          m = x ** 2 + y ** 2 + z ** 2 + x * y + y * z + z * x
          next if n < m
          @a[m] += 1
        end
      end
    end
  end

  def show(ans)
    1.upto(n) do |i|
      puts ans[i]
    end
  end
end

Problem.new.instance_eval do
  show(solve)
end