In mathematics, the Fibonacci numbers, commonly denoted Fn form a sequence, called the Fibonacci sequence, such that each number is the sum of the two preceding ones, starting from 0 and 1. That is,[1]

    F 0 = 0 , F 1 = 1 ,

and

    F n = F n − 1 + F n − 2 ,

for n > 1.

One has F2 = 1. In some books, and particularly in old ones, F0, the "0" is omitted, and the Fibonacci sequence starts with F1 = F2 = 1.[2][3] The beginning of the sequence is thus:

    ( 0 , ) 1 , 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 , 89 , 144 ,...