Some of the new furnaces need very clean power. They have also been known to blow circuit boards with some of the cheap contractor grade generators. I personally like the inverter type of generator that produces true sign wave power. They are also a lot quieter, use less gas and are a lot more expensive. You can run into the same thing with inverters. I have gone with true sign wave inverters and UPS's.
I think you mean sine wave, not sign.