We were discussing Sierpinksi triangles earlier. An equilateral white triangle gets split into four equilateral sub-triangles and the one at the center gets colored red. This process is repeated for all available white squares in each iteration. You are given an integer m for the number of lines following and an integer n in each line following that for the number of iterations for each of which we want an answer.  

What is the total number of triangles after each iteration

We said the recursive solution is as follows:

        static double GetRecursive(int n) 

        { 

         if (n == 0) return 1; 

         return GetRecursive(n-1) + GetRecursive(n-1) + GetRecursive(n-1) 

                    + 1 // for the different colored sub-triangle 

                    + 1; // for the starting triangle

        } 

The same problem can be visualized as  one where the previous step triangle becomes one of the three sub-triangles in the next step.
In this case, we have

    double GetCountRepeated(int n) 

   { 

              double result = 1; 

              for (int i = 0; i < n; i++) 

              { 

                    result = 3 * result 

                                + 1 // for inner triangle 

                                + 1; // for outer triangle

              } 

              return result; 

   }