Fibonacci Series In Python

Python Program to Print the Fibonacci sequence

In this program, you’ll learn to print the Fibonacci sequence using a while loop.

To understand this example, you should have knowledge of the following Python programming topics:

  • Python if…else Statement
  • Python while Loop

A Fibonacci sequence is the integer sequence of 0, 1, 1, 2, 3, 5, 8….

The first two terms are 0 and 1. All other terms are obtained by adding the preceding two terms. This means to say the nth term is the sum of (n-1)th and (n-2)th term.

Source Code

# Program to display the Fibonacci sequence up to n-th term

nterms = int(input("How many terms? "))

# first two terms
n1, n2 = 0, 1
count = 0

# check if the number of terms is valid
if nterms <= 0:
   print("Please enter a positive integer")
elif nterms == 1:
   print("Fibonacci sequence upto",nterms,":")
   print(n1)
else:
   print("Fibonacci sequence:")
   while count < nterms:
       print(n1)
       nth = n1 + n2
       # update values
       n1 = n2
       n2 = nth
       count += 1

Output

How many terms? 7
Fibonacci sequence:
0
1
1
2
3
5
8

Here, we store the number of terms in nterms. We initialize the first term to 0 and the second term to 1.

If the number of terms is more than 2, we use a while loop to find the next term in the sequence by adding the preceding two terms. We then interchange the variables (update it) and continue on with the process.

You can also solve this problem using recursion: Python program to print the Fibonacci sequence using recursion.

Python Program for Fibonacci numbers
  • Difficulty Level: Easy
  • Last Updated: 20 Jan 2021

The Fibonacci numbers are the numbers in the following integer sequence.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..
In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

    Fn = Fn-1 + Fn-2

with seed values

   F0 = 0 and F1 = 1.

Method 1 ( Use recursion ) :

# Function for nth Fibonacci number
def Fibonacci(n):
# Check if input is 0 then it will
# print incorrect input
if n < 0:
print("Incorrect input")
# Check if n is 0
# then it will return 0
elif n == 0:
return 0
# Check if n is 1,2
# it will return 1
elif n == 1 or n == 2:
return 1
else:
return Fibonacci(n-1) + Fibonacci(n-2)
# Driver Program
print(Fibonacci(9))
# This code is contributed by Saket Modi
# then corrected and improved by Himanshu Kanojiya
Output

34

Method 2 ( Use Dynamic Programming ) :

# Function for nth fibonacci
# number - Dynamic Programing
# Taking 1st two fibonacci nubers as 0 and 1
FibArray = [0, 1]
def fibonacci(n):
# Check is n is less
# than 0
if n <= 0:
print("Incorrect input")
# Check is n is less
# than len(FibArray)
elif n <= len(FibArray):
return FibArray[n - 1]
else:
temp_fib = fibonacci(n - 1) +
fibonacci(n - 2)
FibArray.append(temp_fib)
return temp_fib
# Driver Program
print(fibonacci(9))
# This code is contributed by Saket Modi
Output

21

Method 3 ( Space Optimized):

__________________________________

# Function for nth fibonacci
# number - Space Optimisataion
# Taking 1st two fibonacci numbers as 0 and 1
def fibonacci(n):
a = 0
b = 1
# Check is n is less
# than 0
if n < 0:
print("Incorrect input")
# Check is n is equal
# to 0
elif n == 0:
return 0
# Check if n is equal to 1
elif n == 1:
return b
else:
for i in range(1, n):
c = a + b
a = b
b = c
return b
# Driver Program
print(fibonacci(9))
# This code is contributed by Saket Modi
# Then corrected and improved by Himanshu Kanojiya
Output

34

Please refer complete article on Program for Fibonacci numbers for more details!

How do you do the Fibonacci series in Python?

  1. INPUT FORMAT: Input consists of an integer.
  2. OUTPUT FORMAT: …
  3. SAMPLE INPUT: 7.
  4. SAMPLE OUTPUT: 0 1 1 2 3 5 8.
  5. PREREQUISITE KNOWLEDGE: while loop in Python and Recursion in Python. …
  6. Step 1:Input the ‘n’ value until which the Fibonacci series has to be generated.
  7. Step 3:while (count <= n)
  8. Step 5:Increment the count variable.

How do you find the nth Fibonacci number in Python?

Solution Review : Compute nth Fibonacci Number
  1. def fibonacci(n):
  2. if n <= 1:
  3. return n.
  4. else:
  5. return(fibonacci(n-1) + fibonacci(n-2))
  6. print(Fibonacci(4))

What is the Fibonacci Series formula?

Fn = Fn1 + Fn2. to get the rest. Thus the sequence begins 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, … This sequence of Fibonacci numbers arises all over mathematics and also in nature.

What is the logic of the Fibonacci series?

Fibonacci Series is a pattern of numbers where each number is the result of the addition of the previous two consecutive numbers. The first 2 numbers start with 0 and 1. The third numbers in the sequence are 0+1=1. The 4th number is the addition of the 2nd and 3rd number i.e. 1+1=2 and so on.

Is 0 a Fibonacci number?

The Fibonacci sequence is a series of numbers where a number is the addition of the last two numbers, starting with 0, and 1. The Fibonacci Sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…

How do you create Fibonacci numbers?

The Fibonacci Sequence is the series of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The next number is found by adding up the two numbers before it:
  1. the 2 is found by adding the two numbers before it (1+1),
  2. the 3 is found by adding the two numbers before it (1+2),
  3. the 5 is (2+3),
  4. and so on!

What is nth Fibonacci number?

We have only defined the nth Fibonacci number in terms of the two before it: the n-th Fibonacci number is the sum of the (n-1)th and the (n-2)th.

What is the use of the Fibonacci series?

Fibonacci numbers are used to create technical indicators using a mathematical sequence developed by the Italian mathematician, commonly referred to as “Fibonacci,” in the 13th century. The sequence of numbers, starting with zero and one, is created by adding the previous two numbers.

How do you find a number that is Fibonacci or not?

Another method (Quick one) to check if a number if a Fibonacci number or not, is as below: N is a Fibonacci number if and only if ( 5*N2 + 4 ) or ( 5*N2 – 4 ) is a perfect square! For Example, 3 is a Fibonacci number since (5*3*3 + 4) is 49 which is 7*7.

What is the biggest Fibonacci number?

3340367

How do you use the Fibonacci equation?

Add the first term (1) and 0.

This will give you the second number in the sequence. Remember, to find any given number in the Fibonacci sequence, you simply add the two previous numbers in the sequence. To create the sequence, you should think of 0 coming before 1 (the first term), so 1 + 0 = 1.

What does Fibonacci mean in English?

noun. : an integer in the infinite sequence 1, 1, 2, 3, 5, 8, 13, … of which the first two terms are 1 and 1 and each succeeding term is the sum of the two immediately preceding. See the full definition.

What is Fibonacci in Java?

The Fibonacci series is a series where the next term is the sum of the previous two terms. The first two terms of the Fibonacci sequence are 0 followed by 1. The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, …

What are Fibonacci ratios?

They are based on Fibonacci numbers. Each level is associated with a percentage. The percentage is how much of a prior move the price has retraced. The Fibonacci retracement levels are 23.6%, 38.2%, 61.8%, and 78.6%. While not officially a Fibonacci ratio, 50% is also used.

How does Fibonacci recursion work?

Recursion will happen till the bottom of each branch in the tree structure is reached with the resulting value of 1 or 0. During recursion these 1’s and 0’s are added till the value of the Fibonacci number is calculated and returned to the code called the Fibonacci method in the first place.

What is Fibonacci series in C++?

The Fibonacci sequence is a series where the next term is the sum of the previous two terms. The first two terms of the Fibonacci sequence is 0 followed by 1. The Fibonacci sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21.

How did Leonardo Fibonacci discover the Fibonacci sequence?

He noted that, after each monthly generation, the number of pairs of rabbits increased from 1 to 2 to 3 to 5 to 8 to 13, etc, and identified how the sequence progressed by adding the previous two terms (in mathematical terms, Fn = Fn1 + Fn2), a sequence which could, in theory, extend indefinitely.

Is the Fibonacci sequence infinite?

The surprising answer is that there is an infinite number of Fibonacci numbers with any given number as a factor!

What is the golden ratio in Fibonacci?

The golden ratio is about 1.618, and represented by the Greek letter phi, Φ. The golden ratio is best approximated by the famous “Fibonacci numbers.” Fibonacci numbers are a never-ending sequence starting with 0 and 1, and continuing by adding the previous two numbers.