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# Characteristic polynomials for $K$-Bonacci numbers: what's their name?

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?