What is Fibonacci numbers

In mathematics, the Fibonacci numbers are the following sequence of numbers:

By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s.
In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

with seed values

The Fibonacci sequence is named after Leonardo of Pisa, who was known as Fibonacci (a contraction of filius Bonaccio, "son of Bonaccio".) Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics .
The first 21 Fibonacci numbers (sequence A000045 in OEIS), also denoted as Fn, for n = 0, 1, 2, ... ,20 are: 8 , 9
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
Using the recurrence relation, the sequence can also be extended to negative index n. The result satisfies the equation

Thus the complete sequence is