My code

… was written in C++11 and can be compiled with G++, Clang++, Visual C++. You can download it, too. Or just jump to my GitHub repository.

The code contains #ifdefs to switch between the original problem and the Hackerrank version.
Enable #ifdef ORIGINAL to produce the result for the original problem (default setting for most problems).

       
#include <iostream>
       
#include <vector>
       
#include <cmath>
       
 
       
#define ORIGINAL
       
 
       
// find the first sevens solutions in a few seconds

       
void bruteForce(long long limit)
       
{
       
  for (long long base = 2; base < limit; base += 2)
       
  {
       
    // both right-angled triangles with side lengths L, h, half
       
    auto half = base / 2;
       
 
       
    // two potential solutions
       
    auto height1 = base - 1;
       
    auto height2 = base + 1;
       
 
       
    // compute L1 and L2
       
    auto triangle1 = half * half + height1 * height1;
       
    long long hypo1 = sqrt(triangle1);
       
    if (hypo1 * hypo1 == triangle1)
       
      std::cout << hypo1 << " => b=" << base << " h=" << height1 << " diff=" << (base - height1) << std::endl;
       
 
       
    auto triangle2 = half * half + height2 * height2;
       
    long long hypo2 = sqrt(triangle2);
       
    if (hypo2 * hypo2 == triangle2)
       
      std::cout << hypo2 << " => b=" << base << " h=" << height2 << " diff=" << (base - height2) << std::endl;
       
  }
       
}
       
 
       
int main()
       
{
       
  // precompute the first 10^6 solutions
       
  std::vector<unsigned long long> solutions;
       
 
       
  // the first seven solutions reveal a pattern ...
       
  // 17
       
  // 305 = 17*18 - 1
       
  // 5473 = 305*18 - 17
       
  // 98209 = 5473*18 - 305
       
  // 1762289 = 98209*18 - 5473
       
  // 31622993 = 1762289*18 - 98209
       
  // 567451585 = 31622993*18 - 1762289
       
 
       
#ifdef ORIGINAL
       
  const unsigned int MaxPrecompute = 12;
       
#else
       
  const unsigned int MaxPrecompute = 1000000;
       
#endif
       
 
       
  // first solution is 17
       
  long long current  = 17;
       
  solutions.push_back(current);
       
  // add it to the total
       
  long long sum      = current;
       
 
       
  // previous solution ("zero-th" solution is 1
       
  long long previous =  1;
       
  for (unsigned int i = 2; i <= MaxPrecompute; i++)
       
  {
       
    // one more step ...
       
    auto next = current * 18 - previous;
       
 
       
#ifndef ORIGINAL
       
    // prevent negative numbers
       
    const long long Modulo = 1000000007;
       
    if (next < 0)
       
      next += Modulo;
       
#endif
       
 
       
    // next => current => previous
       
    previous  = current;
       
    current   = next;
       
 
       
    // add solution
       
    sum += current;
       
 
       
#ifndef ORIGINAL
       
    // keep only residue
       
    sum     %= Modulo;
       
    current %= Modulo;
       
#endif
       
 
       
    // store solution
       
    solutions.push_back(sum);
       
  }
       
 
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    unsigned long long smallest = 12;
       
    std::cin >> smallest;
       
 
       
    auto index = smallest - 1;
       
    // not pre-computed ? => abort
       
    if (index >= solutions.size())
       
      return 0;
       
 
       
    // look up result
       
    std::cout << solutions[index] << std::endl;
       
  }
       
 
       
  return 0;
       
}

This solution contains 19 empty lines, 24 comments and 11 preprocessor commands.