16.5.1. Recurrence Condition Derivation

Try these first

1. 1.

   What is a recurrence relation?

   Hint

   Think of how you calculate next numbers in a sequence.

2. 2.

   Define a strictly increasing sequence.

   Hint

   Consider examples within common number sequences.

3. 3.

   What defines a strictly increasing sequence?

   • Each term can be equal.
   • Each term is larger than the last.
   • The first term is always zero.

   Hint

   Look for strict relationships, not just numerical patterns.

4. 4.

   Is the base case necessary for recurrence relations?

   • True
   • False

   Hint

   What happens if we skip foundational definitions?

5. 5.

   Given f(4), calculate the relationship to its predecessors and derive the expected value. Discuss the potential sources of error in your calculations.

   Hint

   What allegories in computing can mislead?

6. 6.

   Explore how changing conditions or parameters of categories affects resulting sequence counts. Provide examples.

   Hint

   Think of experiments with binary outcomes.