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Fibonacci natural number sequence
Formulation 0
A D997: Natural number sequence $F : \mathbb{N} \to \mathbb{N}$ is the Fibonacci natural number sequence if and only if
(1) $F_0 = 0$
(2) $F_1 = 1$
(3) $\forall \, n \geq 2 : F_n = F_{n - 1} + F_{n - 2}$
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}