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>
       
 
       
#define ORIGINAL
       
 
       
// memoized solutions

       
const long long Unknown = -1;
       
std::vector<long long> solutions;
       
 
       
// print result modulo some number

       
#ifndef ORIGINAL
       
const unsigned long long Modulo = 1000000007;
       
#endif
       
 
       
// find result for row with a certain length

       
unsigned long long count(unsigned long long space, unsigned int minBlockLength)
       
{
       
  // finished ?
       
  if (space == 0)
       
    return 1;
       
 
       
  // already know the answer ?
       
  if (solutions[space] != Unknown)
       
    return solutions[space];
       
 
       
  // one option is to leave the next cell black
       
  auto result = count(space - 1, minBlockLength);
       
  // insert red blocks at the current position with all possible spaces
       
  for (auto block = minBlockLength; block <= space; block++)
       
  {
       
    // how much is left after inserting ?
       
    auto next = space - block;
       
    // must be followed by a black cell
       
    if (next > 0)
       
      next--;
       
 
       
    // count all combinations
       
    result += count(next, minBlockLength);
       
  }
       
 
       
  // Hackerrank only
       
#ifndef ORIGINAL
       
  result %= Modulo;
       
#endif
       
 
       
  // memoize result
       
  solutions[space] = result;
       
  return result;
       
}
       
 
       
int main()
       
{
       
  // minimum length of each red block
       
  unsigned int       minBlockLength =  3;
       
  // size of the whole row
       
  unsigned long long totalLength    = 50;
       
  std::cin >> totalLength >> minBlockLength;
       
 
       
  // cached results
       
  solutions.resize(totalLength + 1, Unknown);
       
 
       
  // let's go !
       
  std::cout << count(totalLength, minBlockLength) << std::endl;
       
 
       
  return 0;
       
}

This solution contains 13 empty lines, 16 comments and 7 preprocessor commands.