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Fibonacci sequence
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Fibonacci sequence

Entire infinite integer series where the next number is the sum of the two preceding it (0,1,1,2,3,5,8,13,21,...)

Entityconstant-recursive sequenceLucas sequencedivisibility sequenceQ23835349

Also known as Un(1,−1) · Fibonacci series

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36 statements · 17% with external sources · numbers in brackets are citations

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Defining formula
  • \begin{align} F_n = F_{n-1} + F_{n-2},\!\ \\ F_1 = 1, F_2 = 1 \\ \text{or } F_0 = 0, F_1 = 1 \end{align}
  • F_n = \frac{1}{\sqrt{5}} \left( \left( \frac{1 + \sqrt{5} }{2}\right)^n -\left(\frac{1 - \sqrt{5}}{2}\right)^n \right) statement is subject of: Cauchy–Binet formula
  • f(x)=\frac{x}{1-x-x^2}
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22 identifiers linking Fibonacci sequence across the web's reference databases