You are painting a block of flats, each level must be painted either black or white, but you can only paint a level white if it has a black level immediately below it. How many ways are there of painting an $n$-storey block of flats?
I'm struggling with the problem above. I have been introduced to permutations, but have no idea how to use/change the formula to take the restrictions into account. I know level 1 must be black, level 2 could be black or white and there will be three different ways of painting a 3-storey building. I can see that there will be five different ways of painting a 4-storey building (bbbb, bbbw, bbwb, bwbw, bwbb), but maybe I've just not learnt enough to tackle this problem! Any help would be appreciated.