[ Fibonacci Numbers ]

What are the Fibonacci numbers with negative indices $F_{-1}, F_{-2}, \ldots, F_{-n}, \ldots ?$
From the initial conditions $F_{0}=0, F_{1}=1$ and the recurrence relation $F_{\mathrm{n}+2}=F_{\mathrm{n}+1}+F_{\mathrm{n}}$, the Fibonacci numbers with negative indices are uniquely determined: $F_{-\mathrm{n}}=(-1)^{\mathrm{n}+1} F_{\mathrm{n}}$.

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