I'm doing a problem involving a recursive expression, and I'm not quite sure how to accurately show one on paper. I've done some research and looked at other questions but I'm still slightly confused.
The problem in particular is:
The sequence $D_n$ shows the number of ways to color a buildings floor (of $n \ge 1$ stories). Each floor may be yellow or blue, but no blue floors can be touching. Yellow has no restriction. Find a recursive expression for $D_n$ with appropriate initial conditions.
I know how I would solve the problem, but I want to able to write this problem correctly, What are the initial conditions? I have no clue what those are. Thanks for helping!
I would solve this problem by looking at a building of height h, I know that this tower is equal to h-1 + the current floor... I don't know EXACTLY how to solve it as I haven't put in the thought into it yet. I understand what a recursive expression is, I just have no idea what one consists of (the format) is what I really need. It also asks for sufficient initial conditions, and I don't know what initial conditions are.