Divide and conquer: Why F(0) = 0?

by user10511500   Last Updated October 16, 2018 09:20 AM

Reading algorithms. fibonacci example.

I saw an example where it said F(1) =1 and F(0) = 0. (fibonacci)

Why F(1) =1 and F(0) = 0? From where does it originate?


Answers 1

The initialization with $F(0)=F(1)=0$ is pretty fine. The recursion $F(n+1) = F(n)+F(n-1)$ for $n\geq 1$ gives $F(2)=1$, $F(3)=2$ and so on. This definition defines the sequence $(F(n))_n$ for all $n\geq 0$. The sequence is 0,1,1,2,3,5,8, and so on. It can also be written without the initial term: 1,1,2,3,5,8, and so on.

October 16, 2018 08:52 AM

Related Questions

Recursive Fibonacci expressed differently

Updated November 21, 2017 15:20 PM

Algorithm for Converting Rational Into Surreal Number

Updated November 09, 2017 04:20 AM

Fibonacci Sequence golden ratio big O proof

Updated September 30, 2017 05:20 AM