ThmDex – An index of mathematical definitions, results, and conjectures.
F7924
Formulation 1
Let $F : \mathbb{N} \to \mathbb{N}$ be a D997: Natural number sequence such that
(i) $F_0 = 0$
(ii) $F_1 = 1$
Then $F$ is the Fibonacci natural number sequence if and only if \begin{equation} F_2 = F_1 + F_0, \quad F_3 = F_2 + F_1, \quad F_4 = F_3 + F_2, \quad \dots \end{equation}