Scores of stalled construction projects can be found scattered around New York City, but one category of building that doesn’t seem to have been sidetracked by the recession is the luxury apartment rental. At least 16 new rental buildings are expected to open in Manhattan in coming months, ranging from small buildings to 500-unit high-rises, for a total of more than 3,500 apartments. Brooklyn will get an additional 3,500 new apartments as well, including units in some buildings that opened in late 2009.