Python Program to Display Fibonacci Sequence Using Recursion

The Fibonacci sequence is a series where each number is the sum of the two preceding numbers, starting from 0 and 1. We can generate this sequence using recursion, where a function calls itself until it reaches a base case.

Fibonacci Recursion Logic

The recursive approach works by breaking down the problem:

• Base case: If n ? 1, return n
• Recursive case: Return fibonacci(n-1) + fibonacci(n-2)

Example

def fibonacci_recursion(n):
    if n <= 1:
        return n
    else:
        return fibonacci_recursion(n-1) + fibonacci_recursion(n-2)

num_terms = 12

if num_terms <= 0:
    print("Enter a positive integer")
else:
    print("The fibonacci sequence is:")
    for i in range(num_terms):
        print(fibonacci_recursion(i))

Output

The fibonacci sequence is:
0
1
1
2
3
5
8
13
21
34
55
89

How It Works

Let's trace how fibonacci_recursion(4) works:

Performance Consideration

While elegant, recursive Fibonacci has exponential time complexity O(2^n) due to repeated calculations. For large values, consider using memoization or iteration for better performance.

Conclusion

Recursive Fibonacci demonstrates the power of recursion by breaking complex problems into simpler subproblems. However, for practical applications, consider optimized approaches like memoization to avoid redundant calculations.