13.4. Initial Conditions for Recurrence Function

Try these first

1. 1.

   What is the value of F(1) based on the definition given?

   Hint

   Think about the possible one-bit strings.

2. 2.

   List the valid strings for F(2).

   Hint

   Consider combinations of two bits.

3. 3.

   What does F(n) represent in our case?

   • Number of valid bit strings of length n
   • Number of permutations
   • The value of n

   Hint

   Recall what we are counting.

4. 4.

   Is the initial condition for F(1) equal to 1?

   • True
   • False

   Hint

   What are the possible one-bit strings?

5. 5.

   Calculate F(6) and validate all possible strings allowed under the conditions set.

   Hint

   Continue building from F(5) and F(4).

6. 6.

   Discuss how changes to the condition (like allowing '00') would affect your recurrence and outcomes.

   Hint

   Think of all possible combinations!