My code

… was written in C++ and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

       
#include <iostream>
       
#include <vector>
       
#include <algorithm>
       
 
       
int main()
       
{
       
  const unsigned int limit = 1000000;
       
 
       
  // count different layouts for a number of tiles
       
  std::vector<unsigned int> solutions(limit + 1, 0);
       
 
       
  // start with smallest outer ring
       
  for (unsigned int outer = 3; ; outer++)
       
  {
       
    unsigned int sum = 0;
       
    // add as many inner rings as possible
       
    for (unsigned int inner = outer; inner >= 3; inner -= 2)
       
    {
       
      // tiles needed to create one ring whose sides are "inner" tiles long
       
      unsigned int ring = 4 * (inner - 1);
       
 
       
      // runnng out of tiles ?
       
      if (sum + ring > limit)
       
        break;
       
 
       
      // add valid ring
       
      sum += ring;
       
      solutions[sum]++;
       
    }
       
 
       
    // no more inner rings possible, abort
       
    if (sum == 0)
       
      break;
       
  }
       
 
       
  // pre-process all possible answers
       
  std::vector<unsigned int> result(solutions.size());
       
  unsigned int one2ten = 0;
       
  for (unsigned int i = 0; i < solutions.size(); i++)
       
  {
       
    auto s = solutions[i];
       
    if (s >= 1 && s <= 10)
       
      one2ten++;
       
 
       
    result[i] = one2ten;
       
  }
       
 
       
  // process test cases
       
  unsigned int tests;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    unsigned int last = limit;
       
    std::cin >> last;
       
    // simple lookup
       
    std::cout << result[last] << std::endl;
       
  }
       
 
       
  return 0;
       
}

This solution contains 10 empty lines, 10 comments and 3 preprocessor commands.