In the Fibonacci sequence, is fib(0) 0 or 1 ?

Question

I\'m doing a task in a subject were fib(0) is defined to = 1. But that can\'t be right? fib(0) is 0?

Program with fib(0) = 1; spits out fib(4) = 5
Program w         


        

Answer 1

They are both correct. If you specify a sequence G{n} by the recursion G{1} = 3, G{2} = 5, G{n} = G{ n - 1} + G{ n - 2} then most people would agree that is "a Fibonacci sequence". The only difference being a few terms at the front, but the leading terms are mostly irrelevant for any interesting questions about the sequence. The heart of a Fibonacci sequence is the addition rule, and any sequence that uses that rule is a Fibonacci sequence. It is only necessary to specify whether 0 is in the sequence if you want to ask specific questions about a particular index... every thing else is just a translation on the index and is pretty much irrelevant. That is, if the problem is 'find a closed form solution for the Nth value in the sequence', then solving it for G will solve the problem for F with just a trivial shift of the solution. The hard part of the problem is the same for both sequences.