# 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.