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.

       
#include <vector>
       
#include <iostream>
       
#include <algorithm>
       
 
       
// return true if x is a palindrome

       
bool isPalindrome(unsigned int x)
       
{
       
  auto reduced = x / 10;
       
  auto reverse = x % 10;
       
  // fast exit: a trailing zero can't create a palindrome
       
  if (reverse == 0)
       
    return false;
       
 
       
  while (reduced > 0)
       
  {
       
    // chop off the lowest digit and append it to "reverse"
       
    reverse *= 10;
       
    reverse += reduced % 10;
       
    reduced /= 10;
       
  }
       
 
       
  // palindrome ? both must be equal
       
  return reverse == x;
       
}
       
 
       
 
       
int main()
       
{
       
  unsigned int tests = 1;
       
  std::cin >> tests;
       
  while (tests--)
       
  {
       
    unsigned int limit  = 100000000;
       
    unsigned int stride = 1; // distance between consecutive square numbers
       
 
       
    std::cin >> limit >> stride;
       
 
       
    std::vector<unsigned int> solutions;
       
    for (unsigned long long first = 1; 2*first*first < limit; first++)
       
    {
       
      auto next = first + stride;
       
      // sum of a^2 + b^2 + ...
       
      auto current = first * first + next * next;
       
      // still within the limit ?
       
      while (current < limit)
       
      {
       
        // check
       
        if (isPalindrome(current))
       
          solutions.push_back(current);
       
 
       
        // add one element to the sequence
       
        next    += stride;
       
        current += next * next;
       
      }
       
    }
       
 
       
    // sort ...
       
    std::sort(solutions.begin(), solutions.end());
       
    // .. and remove duplicates
       
    auto garbage = std::unique(solutions.begin(), solutions.end());
       
    solutions.erase(garbage, solutions.end());
       
 
       
    // count all solutions
       
    unsigned long long sum = 0;
       
    for (auto x : solutions)
       
      sum += x;
       
 
       
    std::cout << sum << std::endl;
       
  }
       
 
       
  return 0;
       
}

This solution contains 12 empty lines, 11 comments and 3 preprocessor commands.