16.4.1. Recurrence Condition

Try these first

1. 1.

   List the valid sequences for k=1.

   Hint

   Think about what starts and ends.

2. 2.

   What is the count of valid sequences for k=2?

   Hint

   Consider the sequence length.

3. 3.

   What is the recurrence relation derived for s(k)?

   Hint

   Recall how we reduce the structure.

4. 4.

   Is the following statement true? 'For k=2, s(2) = 0.'

   Hint

   What is the only sequence that starts and ends with 1 and 2?

5. 5.

   Derive the relation for s(k) for k=5 using the recurrence and initial conditions established.

   Hint

   Start from already known values.

6. 6.

   Explore how altering the rules for valid sequences changes the recurrence relation established.

   Hint

   What new rules would you propose?