Clash-free rhythms

Problem

Nico is learning the drums and wants to try every rhythm that fits in a bar of n beats. On each beat he either hits or rests, but his teacher gave him a rule: never two hits in a row, because his hands are not that fast yet.

Write a function that takes n, a whole number from 0 up, and returns a list of every rhythm that follows the rule, with no repeats. Each rhythm is a string of n characters: "x" is a hit and "." is a rest. The list goes in alphabetical order, where the dot comes before the x. The bar does not wrap around: a rhythm can start and end with a hit.

With n equal to 3 it returns ["...", "..x", ".x.", "x..", "x.x"]: "xx.", ".xx" and "xxx" are left out because they have two hits in a row. With n equal to 1 it returns [".", "x"]. With n equal to 0 there is a single rhythm, the one with no beats: it returns [""].

Examples

• The three-beat example

  3 → ["...", "..x", ".x.", "x..", "x.x"]

• One beat

  1 → [".", "x"]

• Four beats

  4 → ["....", "...x", "..x.", ".x..", ".x.x", "x...", "x..x", "x.x."]

• No beats

  0 → [""]

Besides these, the challenge has hidden tests that are revealed when you submit your solution.

You start with this

def rhythms(n):
    pass

function rhythms(n) {
}