Generalizations of Fibonacci numbers

In mathematics, the Fibonacci numbers form a sequence defined recursively by:

${\displaystyle F_{n}={\begin{cases}0&n=0\\1&n=1\\F_{n-1}+F_{n-2}&n>1\end{cases}}}$

That is, after two starting values, each number is the sum of the two preceding numbers.

The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers.