Fibonacci numbers are defined by the recurrence relation
$f\_{n+2}=f\_{n+1}+f\_{n}$ and
Tribonacci numbers by
$f\_{n+3}=f\_{n+2}+f\_{n+1}+f\_{n}$


One can define, in general, K-Bonacci numbers as
$f\_{n+K}=f\_{n+K-1}+...+f\_{n+1}+f\_{n}$


(they show up naturally if you consider the problem of counting binary strings of length n which do not contain sequences of K adjacent zeroes).


The characteristic polynomial associated to K-Bonacci numbers is
$$P\_K(t):=t^K-(t^{K-1}+t^{K-2}+...+t+1)$$
By the way, he same polynomial turns up when trying to calculate the asymptotic growth rate via generating functions and, as $K \to +\infty$, the biggest real root approaches 2.


Question: **do these polynomials have a already a name?**



Characteristic polynomials for $K$-Bonacci numbers: what's their name?
The dominant root of such a polynomial is often referred to as a **multinacci number**. These numbers are known to be [Pisot numbers](http://mathworld.wolfram.com/PisotNumber.html) and, indeed, tend to 2. 


