Robert wrote:

> It seems we should call these categories Fibonacci and Pell. Is that something people do?

No, not as far as I've ever heard. I like it, though.

**Puzzle.** There's another famous sequence, the **[Lucas numbers](https://en.wikipedia.org/wiki/Lucas_number)**, also defined by a linear recurrence:

\[ L_0 = 2,\quad L_1 = 1,\quad L_{n+2} = L_{n+1} + L_n \]

Can we get this sequence as the number of loops of length \\(n\\) starting and ending at some chosen node in a graph? If not, can we do it for a shifted version of this sequence? Or can we get it as the number of paths of length \\(n\\) starting at some chosen node and ending at some _other_ chosen node of a graph?

[A study of 657 sunflowers](http://rsos.royalsocietypublishing.org/content/3/5/160091) show that most of them have Fibonacci numbers of spirals, while some have Lucas numbers.

> It seems we should call these categories Fibonacci and Pell. Is that something people do?

No, not as far as I've ever heard. I like it, though.

**Puzzle.** There's another famous sequence, the **[Lucas numbers](https://en.wikipedia.org/wiki/Lucas_number)**, also defined by a linear recurrence:

\[ L_0 = 2,\quad L_1 = 1,\quad L_{n+2} = L_{n+1} + L_n \]

Can we get this sequence as the number of loops of length \\(n\\) starting and ending at some chosen node in a graph? If not, can we do it for a shifted version of this sequence? Or can we get it as the number of paths of length \\(n\\) starting at some chosen node and ending at some _other_ chosen node of a graph?

[A study of 657 sunflowers](http://rsos.royalsocietypublishing.org/content/3/5/160091) show that most of them have Fibonacci numbers of spirals, while some have Lucas numbers.