# Combinatorics based binary sequence

We all know the standard base-$$2$$ representation of integers and many of you will know of Gray codes. Does anybody know of a name (or something I can use to find a good reference) for a method of sequencing a binary representation so that numbers higher in the sequence have more bits set? For example,

$$000, 001, 010, 100, 011, 101, 110, 111.$$

We set $$i$$ bits until all $$n \choose i$$ combinations are used, then increment $$i$$. Does this sequence have a name?