In the Fibonacci sequence, is fib(0) 0 or 1 ?
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 with fib(0) = 0; spits out fib(3) = 3
What is the correct definition?
Answer
The definition with Fib(0) = 1 is known as the combinatorial definition, and Fib(0) = 0 is the classical definition. Both are used in the Fibonacci Quarterly, though authors that use the combinatorial definition need to add a sentence of explanation. Benjamin and Quinn in Proofs that Really Count use f_n for the nth combinatorial Fibonacci number and F_n for the nth classical Fibonacci number. The combinatorial definition is good, not surprisingly for counting questions like "How many ways are there to walk up a flight of n steps, taking either one or two steps at a time?" When n is 0, there's one way to do it, not zero ways.