# Generating first ten numbers of Pell series in Python

In this tutorial, you will learn about Pell Series and how to generate them in Python.

Let’s get started!

### What are Pell series?

Pell Series is a series where subsequent numbers are the sum of twice the previous number and the number previous to the previous number.

It starts from 1 and 2.

Pell Series: 1,2,5,12,29,70,169,…

Look at the sequence of numbers given above and let us try to relate them to the definition of Pell Series:-

- 1 + 2*2 = 5
- 2 + 5*2 = 12
- 5 + 12 *2 = 29
- 12 + 29*2 = 70
- 29 + 70*2 = 169

and so on…

Now that you have a clear idea of what the Pell Series are, let’s move on to how we shall write the Python code to generate the same.

## Code and Output

**Code in Python:-**

a = 1 b = 2 c = 0 print(a) print(b) for i in range(10): c = a + 2*b a = b b = c print(c)

**Output:-**

1 2 5 12 29 70 169 408 985 2378 5741 13860

Please try to dry run the code by hand and understand how the procedure works before moving on to the solution given below!

### Explanation of the Python Code

- The first number of the series needs to be initialised (a = 1).
- The second number of the series needs to be initialised (b = 2).
- Initialise the variable where we shall generate the series (c = 0).
- Now, print the first two numbers of the series and we shall print the other generated numbers consequently.
- Initiate a for loop to print multiple numbers of the Pell series. We shall be printing 10 numbers in this Python tutorial!
- Add twice the previous number and the number previous to the previous number (c = a + 2*b).
- Swap the previous number to the number previous to the previous number (a = b).
- Swap the generated number to the previous number (b = c).
- Print the generated number.

Write a python code to generate the first 10 terms of the sequence from the

above recurrence relation