Fibonacci sequence
The Fibonacci sequence, discovered by Leonardo Pisano Fibonacci, begins
(Sequence http://www.research.att.com/projects/OEIS?Anum=A000045A000045 in [1]). The th Fibonacci number is generated by adding the previous two. Thus, the Fibonacci sequence has the recurrence relation
with and . This recurrence relation can be solved into the closed form
called the Binet formula, where denotes the golden ratio (and is defined in the same entry). Note that
References
- 1 N. J. A. Sloane, (2004), The On-Line Encyclopedia of Integer Sequences, http://www.research.att.com/ njas/sequences/http://www.research.att.com/ njas/sequences/.
Title | Fibonacci sequence |
Canonical name | FibonacciSequence |
Date of creation | 2013-03-22 11:56:07 |
Last modified on | 2013-03-22 11:56:07 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 21 |
Author | Koro (127) |
Entry type | Definition |
Classification | msc 11B39 |
Synonym | Fibonacci number |
Related topic | HogattTheorem |
Related topic | LucasNumbers |
Related topic | ZeckendorfsTheorem |
Related topic | ApplicationsOfSecondOrderRecurrenceRelationFormula |
Defines | Binet formula |