Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contains no consecutive $$0s$$.

Which of the following recurrences does $${x_n}$$ satisfy?

Let $${x_n}$$ denote the number of binary strings of length $$n$$ that contain no consecutive $$0s$$.

The value of $${x_5}$$ is

What is the chromatic number of the following graph?

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve $$3{x^4} - 16{x^3} + 24{x^2} + 37$$ is