The Hierarchy of Integer Sequences is an introduction to combinatorics through the lens of integer sequences. It proceeds up the hierarchy, from relatively simple sequences to more sophisticated sequences, exploring the relationship between the complexity of a sequence and the complexity of the objects it counts.
Access a pdf here.
Roughly half is written. This is enough material for a one-semester undergraduate course in combinatorics. A second half is planned. It will be some time before the second half is finished, so I have decided to post the current draft so that interested people can start making use of it.
Since this is a draft, things will change. Specifically, the numbered questions at the end of each chapter are likely to get assigned different numbers later. Theorem numbers may also change.
Feedback is welcome! If you find an error (or even a minor typo), please please let me know! If you find the book useful, that would also be great to hear. If you are looking forward to reading the second half, that would probably be even better to hear, since it will motivate me to find time to work on it!