Frouf I follow Protein power so I am not aware of the total illegal things for induction with atkins. PP says to eat healthy carbs but does not limit the actual food types you eat. (some are extreemists and will not touch anything that is not totally natural but that is NOT me)
do not worry about the calorie intake right now. it is the least of the worries the first thing to worry about is not being hungry. you body will slow down on the porportions. you need to feel comfortable and enjoy this woe or it will not stick with you!!! or you it. (3 cans of tuna is too much but 2 is just fine)