16.2.3. Recurrence Equation for Bad Strings

Try these first

1. 1.

   What is the value of B(1)?

   Hint

   Think of the possible single-bit strings.

2. 2.

   List three categories of bad strings.

   Hint

   Consider different starting conditions for strings.

3. 3.

   What is the recurrence relation for B(n)?

   • B(n) = B(n-1) + B(n-2) + B(n-3)
   • B(n) = B(n-1)
   • B(n) = B(n-2) + B(n-3)

   Hint

   Recall our categories of bad strings.

4. 4.

   Is B(3) equal to 4?

   • True
   • False

   Hint

   List all valid strings of length 3.

5. 5.

   Calculate B(5) based on previous values.

   Hint

   Keep applying the derived relation repeatedly.

6. 6.

   Provide a comprehensive proof of B(n) as a generating function.

   Hint

   Involve elements from your string category counts.