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Fibonacci numbers

In mathematical terms, the sequence Fn of Fibonacci numbers
F_n = F_{n-1} + F_{n-2},\!\,
with seed values
F_0 = 0 \quad\text{and}\quad F_1 = 1.
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence:
0,\;1,\;1,\;2,\;3,\;5,\;8,\;13,\;21,\;34,\;55,\;89,\;144,\; \ldots\;
By definition, the first two Fibonacci numbers are 0 and 1, and each subsequent number is the sum of the previous two.

 

List of Fibonacci numbers

The first 21 Fibonacci numbers Fn for n = 0, 1, 2, ..., 20 are:
F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20
0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765
The sequence can also be extended to negative index n using the re-arranged recurrence relation
F_{n-2} = F_n - F_{n-1}, \,
which yields the sequence of "negafibonacci" numbers satisfying
F_{-n} = (-1)^{n+1} F_n. \,
Thus the complete sequence is
F−8 F−7 F−6 F−5 F−4 F−3 F−2 F−1 F0 F1 F2 F3 F4 F5 F6 F7 F8
−21 13 −8 5 −3 2 −1 1 0 1 1 2 3 5 8 13 21