  The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is
a function that assigns for each positive integer $n$, the number of distinct
subwords of length $n$ in $w$. The subword complexity of a word is a good
measure of the randomness of the word and gives insight to what the word itself
looks like. In this paper, we discuss the properties of subword complexity
sequences, and consider different variables that influence their shape. We also
compute the number of distinct subword complexity sequences for certain lengths
of words over different alphabets, and state some conjectures about the growth
of these numbers.
