Are you saying you have a standard 20 amp flat blade plug with the blades perpendicular to each other? But the generator only has 15 amp (parallel blades) outlets.. I will give you TWO adapter designs, I recommend the first.
Get a device that among other things is called a Generator Power Maximizer. this device is a molded "puck" only retangular, it has pins that fit in both halves of the 15 amp duplex outlet. You can get them at most major generator stores. Over priced in my humble opinion, and can be a bit hard to find.. I can not find a link on my comptuer just now. THEN get a TT30 (30 amp) Male pigtail and a standard 15/20 DUPLEX outlet.. Job done.. You may have to put crimp on lugs on the 30 amp wire ends (I would recommend it in fact).
Option 2. is a short length of 12ga flexible cord with a standard 15 amp plug on one end and a 15/20 amp outlet on the other, IN fact, I have such a cord here.