Permutations are the most general kind of symmetry. In her talk, Lara Pudwell introduces patterns that permutations can either contain or not contain, and counts how often they appear in some well-known families of permutations. If you do this, then some familiar number series will turn up. When she shows off at the end with some atomic numbers I thought that you, @johncarlosbaez, might like to know that particular result, and I suppose you might also enjoy the rest of this nice lecture!
Lara Pudwell: Patterns in Permutations - MAA MathFest 2023
https://www.youtube.com/watch?v=rxJQ3ZVLRVE
It's easy going and only very little mathematical prerequsites are required.
[#]LaundryLectures
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