16.6.2. Categories of Partitions

Try these first

1. 1.

   Define a strictly increasing sequence.

   Hint

   Think about examples of numbers increasing.

2. 2.

   What is the recurrence relation for valid sequences?

   Hint

   Consider how sequences can build from `n-1`.

3. 3.

   What is a strictly increasing sequence?

   • A sequence where each term is less than the previous term
   • A sequence where each term is the same as the previous term
   • A sequence where each term is greater than the previous term

   Hint

   Think about how numbers progress in a sequence.

4. 4.

   Is the recurrence relation formula f(n) = 2 * f(n-1) correct?

   • True
   • False

   Hint

   Recall the structure of how each term builds.

5. 5.

   Prove that the number of valid sequences for any integer n can be derived using combinations.

   Hint

   Think about how to arrange unique elements.

6. 6.

   Find the total number of valid sequences for n=10 using your recurrence relations.

   Hint

   Keep building on the previous terms!