How

Define a function using recursion

It is possible to define a recursive expression using a recursive function in Python. This requires two things:

• A recursive rule: something that relates the current term to another one;

• A base case: a particular term that does not need the recursive rule to be calculated.

Consider the following mathematical expression:

\[\begin{split} \left\{ \begin{array}{l} a_1 = 1,\\ a_n = 2a_{n - 1}, n > 1, \end{array} \right. \end{split}\]

• The recursive rule is: \(a_n = 2a_{n - 1}\);

• The base case is: \(a_1 = 1\).

In Python this can be written as:

def generate_sequence(n):
    """
    Generate the sequence defined by:

    a_1 = 1
    a_n = 2 a_{n - 1}

    This is done using recursion.
    """
    if n == 1:
        return 1
    return 2 * generate_sequence(n - 1)

Here we can get the first 7 terms:

values_of_sequence = [generate_sequence(n) for n in range(1, 8)]
values_of_sequence

[1, 2, 4, 8, 16, 32, 64]