This question, I am having trouble understanding the recurrence relation, and just the initial condition for this problem. We are currently in chapter 8.1 in Applications of Discrete Mathematics by Rosen if that helps you out. The question is the following image:

Katie has three outt choices while social distancing. Each day she wears either pajamas, sweatpants, or jeans. Her only rule is that she never wears jeans on three or more days in a row. Let an represent the number of ways Katie can choose outts across 1% days (where n 2 0). (a) Find a recurrence relation for an (b) What are the initial conditions for the recurrence relation from part (a)? Note: To earn full credit1 you must have the minimum number of initial conditions as required by your recurrence relation from part (a)