More InductionProofs: strong induction. Sequences.
We also talked about the diagonal Ramsey numbers as an example of a sequence for which we have a definition but we don't know (and probably will never be able to find) all of its values. The sequence starts 1, 2, 6, 18, but subsequent numbers in the sequence are unknown. You don't need to know about Ramsey numbers for the course, but if you want to find out more about them a good starting point is here.
Readings: RosenBook Section 3.2.