16.1.1. Recurrence Condition

Try these first

1. 1.

   Define a recurrence relation for the Fibonacci sequence.

   Hint

   Recall how Fibonacci numbers are derived.

2. 2.

   What is an initial condition for a recurrence relation?

   Hint

   Think about the first term of a sequence.

3. 3.

   What is a recurrence relation?

   • A set of all possible terms
   • An equation defining sequences recursively
   • A way to store sequences

   Hint

   Remember the definition of a sequence.

4. 4.

   True or False: The Fibonacci sequence is an example of a recurrence relation.

   • True
   • False

   Hint

   Think about how Fibonacci numbers are calculated.

5. 5.

   Design a complex recurrence relation for the number of strictly increasing sequences of length 5. Analyze.

   Hint

   Work backwards from the defined term.

6. 6.

   Evaluate the impact of excluding certain patterns from the sequences.

   Hint

   Consider combinations within the context.