16.1. Valid Sequences Analysis

Try these first

1. 1.

   What is a valid sequence for n=3?

   Hint

   Remember what numbers are in increasing order and start with 1 and end with n.

2. 2.

   For n=2, how many valid sequences can you describe?

   Hint

   Think about the definition of valid sequences.

3. 3.

   What does the function f(n) represent?

   Hint

   Think about what constitutes a valid sequence overall.

4. 4.

   What is the recurrence relation we've defined?

   • f(n) = f(n-1)
   • f(n) = 2 * f(n-1)
   • f(n) = f(n-1) + 1

   Hint

   Review how second last term influences the calculation.

5. 5.

   Given f(5) = 4, discuss the structures of valid sequences that exist.

   Hint

   How many ways can numbers be arranged?

6. 6.

   Derive f(n) for n=6 and show all sequences possible.

   Hint

   Construct from earlier instances.