It is titled Challenging Counting problems
There are 13 steps in this staircase. In how many different ways can I climb up this staircase if I can ascend one step at a time, two steps at a time or any combination of one and two steps? Hint: simplify the problem.
I wrote out all the combinations for each stair starting at one and getting one possible out come and added a step to each outcome. I did not finish since once you get to 10 and up there were so many combinations. Is there a simpler way to do this? Thank you fror your help.
read up on partitions.
P(13) = 101
google can provide formulas, and other web sites can provide tables for several values of N.
You can start here. It's an interesting and complicated theory.
mathworld.wolfram.com/PartitionFunctionP.html