Definition:Fibonacci Number/Sequence

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Sequence of Fibonacci Numbers

The sequence of Fibonacci numbers begins:

$0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, \ldots$

This sequence is A000045 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).


Also defined as

The Fibonacci sequence can also be seen defined as:

$1, 1, 2, 3, 5, 8, 13, \ldots$

that is, starting with:

\(\ds F_1\) \(=\) \(\ds 1\)
\(\ds F_2\) \(=\) \(\ds 1\)

instead of with $F_0 = 0$.


Still other sources (and indeed, Fibonacci himself) used:

$1, 2, 3, 5, 8, 13, \ldots$


Sources