Then, count could be a static method, and you wouldn’t need to construct the DominoTilingCounter, yielding

  std::cout << DominoTilingCounter.count(4, 7) << '\n';

That’s close to a free function, using the class only for grouping (say of private helper functions, or for memoization data structures)

In this case you can use a namespace too:

    std::cout << tc::count(4, 7) << '\n';