A rather comprehensive collection of information on floretions, specifically in the context of Oeis, is <A HREF="http://www.mrob.com/pub/seq/floretion.html">Sequences related to floretions.</A> 

> 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 <A HREF="https://en.wikipedia.org/wiki/Quaternion">quaternion</A>, <A HREF="https://en.wikipedia.org/wiki/Octonion">octonion</A> and <A HREF="https://en.wikipedia.org/wiki/Sedenion">sedenion</A> 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, <A HREF="http://fumba.eu/sitelayout/Floretion.html">here you go.</A>