Pumpkin is absolutely okay on induction and I highly recommend for people to use it. (I didn't, but wished I had). It has a lot of fiber, is yummy and nutritious.
Do NOT BE SCARED of carbohydrates, especially those in the form of nutritious vegetables like pumpkin!! Atkins is a low carbohydrate, not NO carbohydrate. Your body, I think you'll find, will do MUCH better at the higher end of the 20 net carb limit if you are getting those carbs from VEGETABLES (especially the "higher" ones like pumpkin, jicama, brussel sprouts, etc.) instead of from eggs, cream, cheese, olives, and the other "special category" foods.
What I've learned (just recently, mind you) is that we get so caught up in this carb phobia that we limit our vegetables, but somehow justify eating "carbs" in the form of sour cream, cream, cream cheese, olives, and stuff like that.
Maybe, just maybe, Dr. A did a little bit of disservice by limiting vegetables so strictly during induction (by cups) because it sets a TONE or gives an impression that vegetables are to be restricted (for the duration of the diet). Then, he doesn't go into enough detail or get descriptive enough when he talks about adding vegetables back during the Ongoing Weight Loss phase.
And, then, the recipe guides don't help allowing shakes, bars, breads, etc. but limiting the vegetables once again (for induction phase)...