title: Friends Pairing Problem 2
signature: function friends_pairing_problem_2(n)
test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return isCorrect(actual,expected)
  end
  
  function driver(n, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(n) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver(24, 17492190577600)
      print(string.format("TEST-0...%s",result))
  
      result = driver(1, 1)
      print(string.format("TEST-1...%s",result))
  
      result = driver(29, 101990226254706560)
      print(string.format("TEST-2...%s",result))
  
      result = driver(3, 4)
      print(string.format("TEST-3...%s",result))
  
      result = driver(14, 2390480)
      print(string.format("TEST-4...%s",result))
  
  end
  
  main()
source_py: def friends_pairing_problem_2(n):
      (a, b, c) = (1, 2, 0)
      if (n <= 2):
          return n
      for i in range(3, (n + 1)):
          c = (b + ((i - 1) * a))
          a = b
          b = c
      return c
source_cpp: int friends_pairing_problem_2(int n) {
    int a = 1, b = 2, c = 0;
    if ( n <= 2 ) {
      return n;
    }
    for ( int i = 3;
    i <= n;
    i ++ ) {
      c = b + ( i - 1 ) * a;
      a = b;
      b = c;
    }
    return c;
  }