Fibonacci sequence

The Fibonacci sequenceMathworldPlanetmath, discovered by Leonardo Pisano Fibonacci, begins


(SequenceMathworldPlanetmath in [1]). The nth Fibonacci number is generated by adding the previous two. Thus, the Fibonacci sequence has the recurrence relation


with f0=0 and f1=1. This recurrence relation can be solved into the closed form


called the Binet formula, where ϕ denotes the golden ratioMathworldPlanetmath (and ϕ is defined in the same entry). Note that



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