Write a Python Program to Print the Fibonacci sequence

The Fibonacci sequence is a series of numbers where each number is the sum of the two preceding ones. It starts with 0 and 1 and continues indefinitely. This sequence appears in mathematics, nature, and computer science.

For example:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

In this tutorial, we will write a Python program to generate the Fibonacci sequence using loops and recursion.

What is the Fibonacci Sequence?

The Fibonacci sequence follows this formula:

Where:

• F(0) = 0, F(1) = 1 (Base cases)
• F(2) = 1 + 0 = 1, F(3) = 1 + 1 = 2, F(4) = 2 + 1 = 3, and so on.

Method 1: Using a Loop (Efficient Approach)

# Taking user input
n = int(input("Enter the number of terms: "))

# First two terms
a, b = 0, 1

if n <= 0:
    print("Please enter a positive integer.")
elif n == 1:
    print("Fibonacci sequence:", a)
else:
    print("Fibonacci sequence:", a, b, end=" ")
    for _ in range(2, n):
        c = a + b
        print(c, end=" ")
        a, b = b, c

Output 1

Enter the number of terms: 8
Fibonacci sequence: 0 1 1 2 3 5 8 13

Output 2

Enter the number of terms: 0
Please enter a positive integer.

Method 2: Using Recursion

def fibonacci(n):
    if n <= 0:
        return "Invalid input. Enter a positive integer."
    elif n == 1:
        return [0]
    elif n == 2:
        return [0, 1]
    else:
        seq = fibonacci(n - 1)
        seq.append(seq[-1] + seq[-2])
        return seq

# Taking user input
n = int(input("Enter the number of terms: "))
print("Fibonacci sequence:", fibonacci(n))

How Recursion Works?

Recursion calls the function repeatedly to calculate each Fibonacci number.
For example, calculating fibonacci(5) works as:

fibonacci(5)=[0, 1, 1, 2, 3]

This method is simpler but less efficient for large numbers due to repeated function calls.

Method 3: Using Python’s Generator (Memory Efficient)

def fibonacci_gen(n):
    a, b = 0, 1
    for _ in range(n):
        yield a
        a, b = b, a + b

# Taking user input
n = int(input("Enter the number of terms: "))

print("Fibonacci sequence:", list(fibonacci_gen(n)))

Generators save memory as they generate values on demand instead of storing the entire sequence.