GamesNovatory/Enigmas/How Much (How Many) ?/Restaurants

The original puzzle
Some restaurants make clients pay according to their means. There is a dollar entrance fee, the meal costs half of the money you have, and there is a tip of a dollar before leaving. How much money did you start with if you have none left after visiting 4 restaurants ?

The Solution
This enigma is quite similar to that of the apples and, once again, we start at the end -
     1. At the fourth restaurant you paid "$1 entrance, 1/2 of your money, and $1 tip"
          and had no money left.
               "1/2 of your money" was evidently $1 to leave the $1 tip
                    so you had $2 before paying the meal plus $1 to get in,
                         $3 on arriving at the restaurant.
     2. At the third restaurant you paid "$1 entrance, 1/2 of your money, and $1 tip"
          and had $3 left.
               "1/2 of your money" was evidently $4 to leave the $1 tip
                    so you had $8 before paying the meal plus $1 to get in,
                         $9 on arriving at the restaurant.
     3. At the second restaurant you paid "$1 entrance, 1/2 of your money, and $1 tip"
          and had $9 left.
               "1/2 of your money" was evidently $10 to leave the $1 tip
                    so you had $20 before paying the meal plus $1 to get in,
                         $21 on arriving at the restaurant.
     4. At the first restaurant you paid "$1 entrance, 1/2 of your money, and $1 tip"
          and had $21 left.
               "1/2 of your money" was evidently $22 to leave the $1 tip
                    so you had $44 before paying the meal plus $1 to get in,
                         $45 on arriving at the restaurant.

Mathematics
The formula for the money required, in terms of the number of reataurants,
     is not as simple as it was for the apples,
          the $1 entrance charge and the $1 tip tripling the rate of increase.
If "n" represents the number of restaurants,
     the number of dollars at the very start will be 3(2n - 1).
               Once again the usual 2n - 1 formula.
          For 10 restaurants you would need $3069, a tidy sum !