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{{Short description|Triangular arrangement of numbers based on the Fibonacci numbers}} ...thor-link=Haruo Hosoya |date=1976 |title=Fibonacci Triangle |journal=[[The Fibonacci Quarterly]] |volume=14 |issue=2 |pages=173–178|doi=10.1080/00150517.1976.12 ...

{{Short description|Mathematical series, portmanteau of "Fibonacci" and "factorial"}} ...is defined as the product of the first {{math|''n''}} positive [[Fibonacci numbers]], i.e. ...

{{Short description|Identity for real numbers}} ...|Geometric interpretation of the Candido identity for sequential Fibonacci numbers. The white area equals the grey area and each of them equals half of the ou ...

{{short description|Infinite matrix of integers derived from the Fibonacci sequence}} ...ccurs exactly once in the array, and every integer sequence defined by the Fibonacci recurrence can be derived by shifting a row of the array. ...

...amount of starting data. It is of the [[Lagged Fibonacci generator|lagged Fibonacci]] type introduced by [[George Marsaglia]] and Arif Zaman in 1991.<ref name= ...to the fact that each random number is a function of two of the preceding numbers at some specified, fixed offsets, or "lags". ...

In [[mathematics]], a [[sequence]] of [[Natural number|natural numbers]] is called a '''complete sequence''' if every positive [[integer]] can be ...]s, since adding even numbers produces only even numbers—no [[even and odd numbers|odd number]] can be formed. ...

...cci word fractal''' is a [[fractal curve]] defined on the plane from the [[Fibonacci word]]. [[File:Fibonacci fractal first iterations.png|thumb|The first iterations]] ...

...+1 into ''k''&hairsp;+1 ordered partitions form [[Pascal's triangle]], the numbers of [[composition (combinatorics)|compositions]] of ''n''&hairsp;+1 into ''k ...l Links Between Sums Over Paths in Bernoulli's Triangles and the Fibonacci Numbers], ''Journal of Integer Sequences'', '''19''' (2016) 16.8.3.</ref> ...

{{Short description|Numbers whose binary representation does not contain two consecutive ones}} In [[mathematics]], the '''fibbinary numbers''' are the numbers whose [[binary representation]] does not contain two consecutive ones. That ...

In [[mathematics]], the '''Fibonomial coefficients''' or '''Fibonacci-binomial coefficients''' are defined as ...0&nbsp;≤&nbsp;''k''&nbsp;≤&nbsp;''n'', ''F_j'' is the ''j''-th [[Fibonacci number]] and ''n''!_F is the ''n''th [[Fibonorial]], i.e. ...

...ref><ref>{{Cite web |title=Lame's Theorem - First Application of Fibonacci Numbers |url=https://www.cut-the-knot.org/blue/LamesTheorem.shtml |access-date=2023 The [[Fibonacci number]]s are defined by <math>F_0=0,</math> <math>F_1=1,</math> and ...

...tion]] of positive integers as a sum of distinct non-consecutive Fibonacci numbers. ...

* The numbers of the form <math>2^n-1</math> ([[Mersenne number]]s) form a strong divisib * The [[repunit]] numbers in any base {{math|''R''_''n''^(b)}} form a strong divi ...

...ns to this counting problem, the so-called Euler zigzag numbers or up/down numbers, are: ...ube]].<ref>{{harvtxt|Gansner|1982}} calls the fact that this lattice has a Fibonacci number of elements a “well known fact,” while {{harvtxt|Stanley|1986}} asks ...

...tilings and colored tilings".{{r|rayburn}} For instance, for the Fibonacci numbers, considering whether a tiling does or does not connect positions <math>a-1< ...] and [[abstract algebra]], and the final chapter returns to the Fibonacci numbers with more advanced material on their identities.{{r|glass}} ...

| journal = [[Fibonacci Quarterly]] The multiples produced by reversing these numbers, such as 9801 or 8712, are sometimes called '''palintiples'''.<ref>{{citati ...

...t=Elena|last=Deza|author-link=Elena Deza|title=Mersenne Numbers And Fermat Numbers|page=263|publisher=World Scientific|year=2021|isbn=978-9811230332}}</ref> ...name=oeis>{{cite OEIS|A052294|mode=cs2}}</ref> The sequence of pernicious numbers begins ...

...n |title=The Brahmagupta polynomials in two complex variables |journal=The Fibonacci Quarterly |date=February 1998 |volume=36 |pages=34–42 |doi=10.1080/00150517 ...rahmagupta's identity]] says that, for given integer N, the product of two numbers of the form <math>x^2 -Ny^2</math> is again a number of the form. More prec ...

...2.svg|thumb|upright=1.5|Generalised dissection of a square using Fibonacci numbers]] ..., 5, 3 (see graphic).<ref name="Koshy">Thomas Koshy: ''Fibonacci and Lucas Numbers with Applications''. Wiley, 2001, {{ISBN|9781118031315}}, pp. 74, 100–108 < ...

...fact that its fusion rules are described by [[Fibonacci sequence|Fibonacci numbers]].<ref name=":0" /> The Fibonacci category <math>{\bf Fib}</math> is defined as follows.<ref name=":6" /> The ...