Corrected Fibonacci series equation

[ZiadAmerr]

Overview

Corrected Fibonacci equation as defined

$$ \displaystyle \mathrm{fib}(x) = \left\{ \begin{array}{ll} {0}, & \mathrm{if} \ {x = {0}} \\ {1}, & \mathrm{if} \ {x = {1}} \\ \mathrm{fib}\left(x - {1}\right) + \mathrm{fib}\left(x - {2}\right), & \mathrm{otherwise} \end{array} \right. $$

and not

$$ \displaystyle \mathrm{fib}(x) = \left\{ \begin{array}{ll} {1}, & \mathrm{if} \ {x = {0}} \\ {1}, & \mathrm{if} \ {x = {1}} \\ \mathrm{fib}\left(x - {1}\right) + \mathrm{fib}\left(x - {2}\right), & \mathrm{otherwise} \end{array} \right. $$

The seeds of the sequence, $fib(0)$ and $fib(1)$ are $0$ and $1$ respectively and NOT $1$ and $1$ respectively.

References

https://oeis.org/A000045

https://www.mathsisfun.com/numbers/fibonacci-sequence.html

https://www.cuemath.com/algebra/fibonacci-numbers/

https://www.collinsdictionary.com/dictionary/english/fibonacci-sequence

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