Difference between revisions 48147019 and 81567909 on enwiki

The '''anti-Fibonacci numbers''' comporise a sequence closely related to the [[Fibonacci sequence]].  It satisfies the following [[recursion]] formula:

:<math>f(k+2) = f(k) - f(k+1)\, .</math>

Usually, it is made to start with 1, 0. Then, it goes like this:The anti-Fibonacci sequence begins

:<math>1,0,1,-1,2,-3,5,-8, \dots\,</math>

For easBy comparison: T, the Fibonacci sequence satisfies the formula

:<math>fF(k+2) = fF(k) + fF(k+1)\,  </math>

and goes like this:begins

:<math>0,1,1,2,3,5,8, \dots\,</math>
 
If theThe anti-Fibonacci sequence also appears if Fibonacci sequence is extended backwards -(below 0)

:<math>\dots -8,5,-3,2,-1,1,0,1,1,2,3,5,8, \dots\,</math>

- the anti-Fibonacci numbers also appear.

While the ratio <math>\frac{f(k+1)}{f(k)}</math> converges to <math>\phi=1.618</math> for the Fibonacci sequence, the ratioWhile the ratio of successive Fibonacci numbers converges on <math>{\phi}\, </math> (the golden ratio), the ratio of successive anti-Fibonacci numbers converges ton <math>-\frac{1}{\phi}=-0.618</math> for the anti-Fibonacci numbers.\,}.</math>

[[Category:Recurrence relations]]
[[Category:Integer sequences]]
[[Category:Fibonacci numbers]]

[[eo:Vikipedio:Projekto matematiko/Kontraŭ-fibonaĉi-aj nombroj]]