While on approach during a repositioning flight, the pilot selected the landing gear to the down position. The right main landing gear failed to extend and after multiple attempts to get the gear to extend, the pilot made the decision to land with the right main gear up. Video of the accident showed a smooth landing on the left main and nose with the right wing settling to the runway. The airplane exited the right side of the runway, and the right wing struck a runway light and a taxiway sign. Upon contact with the sign, the video showed the right main landing gear falling out of the wheel well. The runway excursion resulted in substantial damage to the right wing. An examination of the maintenance records found that prior to the accident flight, the right main wheel and tire was were replaced. When the gear was retracted during the landing gear examination, the tire contacted the outer diameter of the wheel well cutout and the hydraulic system forced it into the well. When selected down, the right main landing gear became stuck on the wheel well cutout and was unable to be extended. Measurement of the tire and 4 four others of the same make, model, and size showed the diameter of the tire to be 0.5 inches larger than the recommended tire. The landing gear was tested with the manufacturer’s recommended tire and the landing gear extended and retracted normally with no binding. Review of the DA-42 maintenance manual found that the minimum clearance of the tire to the outer diameter of the wheel well is was 4 millimeters. With the tire used, having a larger tread radius, this exceeded the 4-millimeter threshold and caused the tire to get stuck. The maintenance manual procedure for replacement of a wheel and tire requires required that the landing gear be retracted and adjusted for this tolerance on every tire change. The technician who changed the tire reported that he did not perform the landing gear retraction and adjustment after changing the tire.