17. New houses are to be built along one side of a street (Leonardo’s Lane), divided into equal-sized lots. Each house is either a single-family detached house, taking up one lot, or a duplex, taking up two lots. Suppose that there are lots on the street. How many different arrangements (orderings) of houses are there, for , and in general? (This exercise was inspired by a puzzle by Paul Dixon at the website by Ron Knott, cited in the Suggested Websites at the end of this chapter.)