## Introduction to Fibonacci Series in Python

Fibonacci series can be explained as a sequence of numbers where the numbers can be formed by adding the previous two numbers. It starts from 1 and can go upto a sequence of any finite set of numbers. It is 1, 1, 2, 3, 5, 8, 13, 21,..etc. As python is designed based on the object oriented concepts, a combination of multiple conditional statements can be used for designing a logic for Fibonacci series. Three types of usual methods for implementing Fibonacci series are ‘using python generators‘, ‘using recursion’, and ‘using for loop’.

**For Example:**

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ..so on

So here 0+1 =1

1+1 = 2

1+2 = 3

2+3 = 5

3+5 = 8

5+8 = 13

8+ 13 = 21 and so on.

Looking at the above, one would have got certain idea about what we are talking about.

However, In terms of mathematical rule, it can be written as:

Where nth number is the sum of the number at places (n-1) and (n-2). When it comes to implementing the Fibonacci series, there could be a number of coding languages through which it could be done.

However, Python is a widely used language nowadays. Let’s see the implementation of the Fibonacci series through Python. One should be aware of basic conditioning statements like the loop, if-else, while loop, etc. in Python, before proceeding here. If not, it would be great if one can revise it and then take up the coming content. Here for demo purpose, I am using spyder which is IDE for python programming language. One can use any other IDE or Ipython notebooks as well for the execution of the Python programs.

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### Fibonacci Series in Python

Let’s see the implementation of Fibonacci number and Series considering 1^{st} two elements of Fibonacci are 0 and 1:

However, you can tweak the function of Fibonacci as per your requirement but see the basics first and gradually move on to others.

#### Python Code for finding nth Fibonacci Number

**Code 1:**

`def Fibonacci_num(m):`

u = 0

v = 1

if m < 0:

print("Incorrect input entered")

elif m == 0:

return u

elif m == 1:

return v

else:

for i in range(2,m):

c = u + v

u = v

v = c

return v

**Code 2:**

**Output:**

As one can see, the Fibonacci number at 9^{th} place would be 21, and at 11^{th} place would be 55.

- Here “fibonacci_num” is a function defined, which takes care of finding the Fibonacci number with the help of certain conditions. This function can be called by specifying any position.

Now let’s see how one can print series till the position mentioned:

**Code:**

**Output:**

One can notice the start of Fibonacci numbers is defined as 0 and 1.

- If someone wants to define their own starting terms, that can also be done in the same way by tweaking n1 and n2. Here is the example for that:

Let’s say now we want our starting terms be: n1 = 3, n2 = 5

So here your 4^{th} term position (user input is taken), will be decided based on your starting terms.

### Methods Through which Fibonacci Series can be Generated

Below are the three methods, through which Fibonacci series can be generated:

#### 1. Through Generators

**Code:**

`def fibo(num):`

a,b = 0, 1

for i in xrange(0, num):

yield "{}:: {}".format(i + 1,a)

a, b = b, a + b

for item in fibo(10):

print item

**Output:**

This method is referred to as “generator” because the function xrange is a generator of the numbers between 0 and num and yield is the generator for formatted output.

**Here is What xrange does for you:**

Here Fibonacci series has been defined in the form of function, inside which for loop, xrange and yield function takes care of the output.

#### 2. Through for loop

**Code:**

`u, v = 0, 1`

for i in xrange(0, 10):

print u

u, v = v, u + v

**Output:**

As one can see, simple for loop has been used, to print the Fibonacci series between 0 to 10. Inside for loop, new values have been assigned to the variables. U and v are the default initial values of Fibonacci that have been set to 0 and 1 respectively.

As for loop progresses to run, the new u value is the old v value, whereas the new v value is the sum of old values of u and v. This continues till the end of range values.

#### 3. Through Recursion

**Code:**

`#Through recursion`

def fibonacci_ser(m):

if(m <= 1):

return m

else:

return(fibonacci_ser(m-1) + fibonacci_ser(m-2))

m = int(input("Enter number of terms:"))

print("Fibonacci sequence:")

for i in range(m):

print fibonacci_ser(i),

**Output:**

- The function “fibonacci_ser” is making the call to itself to print the Fibonacci series.
- And hence the method has got its name “recursion”.

**Steps Followed here:**

- Here the user has been asked to input the place till which Fibonacci series needs to be printed.
- Number passes through the function “fibonacci_ser”.
- The condition gets checked, if the length provided is less than 1 or not. If yes, the result is given immediately.
- However if the length is greater than 1, recursive calls are made to “fibonacci_ser” with arguments having length lesser than 1 and 2 i.e. fibonacci_ser(m-1) and fibonacci_ser(m-2).
- Hence, recursion gives the desired output and print it.

- So, in short, We discussed Three ways for displaying the Fibonacci series.
- Through for loop, through generators and through recursion.

### All Three Python Code’s Summarized

Below are the three python code:

#### 1. Through Generators

**Code:**

`def fibo(num):`

a,b = 0, 1

for i in xrange(0, num):

yield "{}:: {}".format(i + 1,a)

a, b = b, a + b

for item in fibo(10):

print item

#### 2. Through for loop

**Code:**

`u, v = 0, 1`

for i in xrange(0, 10):

print u

u, v = v, u + v

#### 3. Through Recursion

**Code:**

`def fibonacci_ser(n):`

if(n <= 1):

return n

else:

return(fibonacci_ser(n-1) + fibonacci_ser(n-2))

n = int(input("Enter number of terms:"))

print("Fibonacci sequence:")

for i in range(n):

print fibonacci_ser(i),

Summarized above are all procedures, one needs to practice to get a good grip on all.

**Output:**

### Conclusion

Going through the above content of Fibonacci, one would have got crystal clear understanding of Fibonacci numbers and series, specialized with python. Once, one gets comfortable with the logic of the Fibonacci series, generating another set of series, working with other numbers and with various methods will now be a cakewalk for you. A logical approach is the only way to excel in this.

### Recommended Articles

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