Fibonacci Numbers - List, Meaning

At some point during our academics, we all have studied the concept of Fibonacci Numbers.

Fibonacci Numbers are an important topic for students as well as programmers and with the help of Fibonacci Numbers, programmers can solve different coding challenges.

Every programmer should know about the approach to solving Fibonacci Numbers. It is one of the topics through which you will get to understand recursive calls.

Some problems which are based on the Fibonacci Numbers are the sum of Fibonacci numbers, multiplication of Fibonacci numbers, etc. which can be asked in the coding round of some companies.

Anyone here to understand its meaning and list should continue evolving with this guide to learn about Fibonacci Numbers in depth.

What are Fibonacci Numbers?

Fibonacci Numbers are an important concept of mathematics. It is a series of infinite numbers which are aligned in a sequence and follows the same pattern for calculating numbers. The first two numbers of the Fibonacci are 0 and 1. After it, the rest of the numbers are derived by calculating the previous two numbers. However, the first two numbers will be the same for every case.

Let us understand Fibonacci Numbers through examples.

Example

0 1 1 2 3 5 8 13 21 ……

For the given example, the first two numbers are 0 and 1. After it, the next term is calculated by adding the previous two terms. We will get our F(2) by adding F(0) and F(1). Therefore, F(0)=0 and F(1)=1, so by adding it, we will get the F(2) which is 1.

By following the same pattern, we will derive the next Fibonacci number. Now, we will calculate the F(3), by adding F(2) and F(1). It will be 1 + 2 which equals 3, so the F(3) will be 3. We will be doing this on a loop to get the Fibonacci Sequence.

Formula To Find The Fibonacci Numbers

Finding the Fibonacci Numbers is not hard using the proper formula. There is a formula available to calculate the Fibonacci Numbers easily. However, there will be some rules that you will need to follow. We will tell you about it while explaining the formula of Fibonacci Numbers.

Let’s see.

When you are asked to find the Fibonacci Numbers, then you will be given F(n) which you will use to find it. Now, let’s check out the formula for deriving the Fibonacci Number.

Formula

Fn= Fn-1 + Fn-2

By using the given formula, we will be able to calculate the Fibonacci Sequence. Let’s see how we will do it.

From the given Fibonacci numbers: 0 1 1 2 3 5, Calculate the 7th Fibonacci Number(F7).

Here we have, F(0)= 0, F(1)= 1, F(2)= 1, F(3)= 2, F(4)= 3, F(5)= 5.

For calculating the F(7), we will apply the formula. Let’s see.

Fn = Fn-1 + Fn-2

After applying the formula,

F(7)= F(7-1) + F(7-2)

F(7)= F(6) + F(5)

By formula, we have got that we will need the F(6) and F(5) for calculating the F(7). First of all, we will calculate the F(6).

F(6) = F(5) + F(4)

F(6) = 5 + 3 (By putting the value of F(5) and F(4))

F(6) = 8

Now, we have got the F(6). We will continue with our problem.

F(7) = F(6) + F(5)

F(7) = 8 + 5

F(7) = 13.

We have calculated the Fibonacci Number of the given question. By following the formula, we can do this for any given number.

The programmers also follow the same approach for calculating the Fibonacci Sequence. For calculating it, the programmers use the recursive function. The recursive functions are those functions that call itself in every iteration.

By doing this on a consecutive loop, we get the sequence of the Fibonacci Numbers. Similarly, by using the recursive functions, we will be able to calculate the sum of Fibonacci numbers, multiplication of Fibonacci numbers, etc. These are some important operations which you need to practice. After practicing it, you will be able to attempt the house robbers problem.

Important Rules of Fibonacci Numbers

When you will get any term for calculating the Fibonacci Numbers, then you will have to follow some rules for getting the correct answer.

Without following the rule, you will not be able to calculate the Fibonacci number.

The first two numbers of the Fibonacci Numbers will always be 0 and 1. It means the F(0) = 0 and F(1)= 1, therefore don’t get confused with it.

For calculating the Fibonacci of a given number, you will need to know about its previous two terms.

You will need to use the formula for calculating any given Fibonacci Numbers.

After knowing how to calculate the Fibonacci Numbers, let’s check where the Fibonacci numbers are used.

Some Uses Of Fibonacci Numbers

You might be thinking about the uses of Fibonacci Numbers. We are listing some of them below. Make sure to check it.

The Fibonacci Numbers are used to solve some patterns in the coding as well as in different subjects.

With the use of Fibonacci Numbers, we can get to know about the working of recursive functions.

Some petals in the plants like lilies, roses, sunflowers, etc follow the same pattern which is also known as Fibonacci Flowers.

The Starfish and Seashell also follow the pattern of Fibonacci Numbers.

The spirals that we see in the pinecone are equal to the Fibonacci Numbers.

Fibonacci Numbers Lists

Here is the list of Fibonacci Numbers that you should remember.

F(0)= 0

F(1)= 1

F(2)= 1

F(3)= 2

F(4)= 3

F(5)= 5

F(6)= 8

F(7)= 13

F(8)= 21

F(9)= 34

F(10)= 55

F(11)= 89

F(12)= 144

F(13)= 233

F(14)= 377

F(15)= 610

F(16)= 987

F(17)= 1597

F(18)= 2584

F(19)= 4181

Conclusion

Whether you are a technical student or a non-technical student, it is important to know about the Fibonacci Sequence and Lists.

Without the proper knowledge, you will not be able to solve important questions. Make sure to understand the whole concept if you are going to attempt the problem of house robbers. The house robbers problem is based on the Fibonacci number. You will have to solve this problem by using the same approach of the Fibonacci number.