A rather comprehensive collection of information on floretions, specifically in the context of Oeis, is Sequences related to floretions.
In essence, most of the "floretion" sequences come from an iterated function that begins with some initial value and produces one integer at each step of the iteration. The floretion algorithms operate on a 16-element quantity that can be thought of a a $4\times 4$ matrix. Such a 16-element quantity is called a floretion. The name is deliberately similar to quaternion, octonion and sedenion because the operations performed with them are similar. (But why doesn't the floretion have its own Wikipedia page?)
If you want to "hear" a floretion, here you go.