Definition:Fibonacci Number/Sequence/Negative
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Sequence of Fibonacci Numbers for Negative Index
The sequence of Fibonacci numbers for negative index begins:
- $\ldots, 89, -55, 34, -21, 13, -8, 5, -3, 2, -1, 1, 0$
This sequence is A039834 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1957: George Bergman: Number System with an Irrational Base (Math. Mag. Vol. 31, no. 2: pp. 98 – 110) www.jstor.org/stable/3029218
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.8$: Fibonacci Numbers: Exercise $8$