Generating the Fibonacci sequence is a classic recursive problem. Remove ads Examining the Recursion Behind the Fibonacci Sequence The algorithm remains the same because you’re always summing the previous two numbers to get the next number in the sequence.įor the purposes of this tutorial, you’ll use the version of the sequence that starts with 0. In this alternative version, F(0) is still implicitly 0, but you start from F(1) and F(2) instead. There’s also a version of the sequence where the first two numbers are both 1, like so: In mathematical terminology, you’d call this a recurrence relation, meaning that each term of the sequence (beyond 0 and 1) is a function of the preceding terms. Indian mathematicians had known about this sequence since the sixth century, and Fibonacci leveraged it to calculate the growth of rabbit populations.į( n) is used to indicate the number of pairs of rabbits present in month n, so the sequence can be expressed like this: The pattern begins after the first two numbers, 0 and 1, where each number in the sequence is always the sum of the two numbers before it. Leonardo Fibonacci was an Italian mathematician who was able to quickly produce an answer to this question asked by Emperor Frederick II of Swabia: “How many pairs of rabbits are obtained in a year, excluding cases of death, supposing that each couple gives birth to another couple every month and that the youngest couples are able to reproduce already at the second month of life?” Getting Started With the Fibonacci Sequence
Having some familiarity with these concepts will greatly help you understand the new ones you’ll be exploring in this tutorial.įree Download: Get a sample chapter from Python Basics: A Practical Introduction to Python 3 to see how you can go from beginner to intermediate in Python with a complete curriculum, up-to-date for Python 3.8. To get the most out of this tutorial, you should know the basics of Big O notation, object-oriented programming, Python’s special methods, conditional statements, functions, and basic data structures like lists, queues, and stacks.
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In this tutorial, you’ll focus on learning what the Fibonacci sequence is and how to generate it using Python. Learning how to generate it is an essential step in the pragmatic programmer’s journey toward mastering recursion. The sequence comes up naturally in many problems and has a nice recursive definition. The Fibonacci sequence is a pretty famous sequence of integer numbers. Watch it together with the written tutorial to deepen your understanding: Exploring the Fibonacci Sequence With Python Watch Now This tutorial has a related video course created by the Real Python team.
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