Python Program to Generate first N numbers of Pell Series

Pell series – Python Program to Generate first N numbers of Pell Series

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Pell series: Given the number N, the task is to print the first n numbers of the pell series in Python.

Pell Series:

The Pell Series is a series in which the next number equals the sum of twice the previous number and the number preceding the previous number.

It begins with 1 and 2.

Pell Numbers: 1,2,5,12,29,70,169,…

Consider the following number sequence and try to match it to the definition of the Pell Series:

1 + 2 x 2 = 5

2 + 5* 2 = 12

5 + 12 x 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.

Examples:

Example1:

Given number = 12

Input:

The first 12 numbers of the pell series are :
1 2 5 12 29 70 169 408 985 2378 5741 13860

Output:

Example2:

Input:

Given number = 21

Output:

The first 21 numbers of the pell series are :
1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
 15994428 38613965

Program to Generate first N numbers of Pell Series in Python

Below are the ways to generate the first N number of the pell series in Python.

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Method #1: Using For Loop (Static Input)

Approach:

  • Give the number N as static input and store it in a variable.
  • Take a variable temp1 and initialize it to 1.
  • Take another variable temp2 and initialize it to 2.
  • Take the third variable temp3 and initialize it to 0.
  • Now, print the first two numbers in the series, and we’ll print the other generated numbers in the order they were generated.
  • Loop till number -2 using For loop.
  • Add the value of temp1 and twice the temp2 value and initialize the temp3 with this value.
  • Swap the previous number for the previous number’s predecessor (temp1 =temp2).
  • Swap the generated and previously generated numbers (temp2 = temp3).
  • Print the value of temp3.
  • The Exit of the Program.

Below is the implementation:

# Give the number N as static input and store it in a variable.
numb = 21
# Take a variable temp1 and initialize it to 1.
temp1 = 1
# Take another variable temp2 and initialize it to 2.
temp2 = 2
# Take the third variable temp3 and initialize it to 0.
temp3 = 0
# Now, print the first two numbers in the series,
# and we'll print the other generated numbers in the order they were generated.
print('The first', numb, 'numbers of the pell series are :')
print(temp1, temp2, end=' ')
# Loop till number -2 using For loop.
for i in range(numb-2):
    # Add the value of temp1 and twice the temp2 value
    # and initialize the temp3 with this value.
    temp3 = temp1+2*temp2
    # Swap the previous number for the previous number's predecessor (temp1 =temp2).
    temp1 = temp2
    # Swap the generated and previously generated numbers (temp2 = temp3)
    temp2 = temp3
    # Print the value of temp3.
    print(temp3, end=' ')

Output:

The first 21 numbers of the pell series are :
1 2 5 12 29 70 169 408 985 2378 5741 13860 33461 80782 195025 470832 1136689 2744210 6625109
 15994428 38613965

Method #2: Using For Loop (User Input)

Approach:

  • Give the number N as user input using int(input()) and store it in a variable.
  • Take a variable temp1 and initialize it to 1.
  • Take another variable temp2 and initialize it to 2.
  • Take the third variable temp3 and initialize it to 0.
  • Now, print the first two numbers in the series, and we’ll print the other generated numbers in the order they were generated.
  • Loop till number -2 using For loop.
  • Add the value of temp1 and twice the temp2 value and initialize the temp3 with this value.
  • Swap the previous number for the previous number’s predecessor (temp1 =temp2).
  • Swap the generated and previously generated numbers (temp2 = temp3).
  • Print the value of temp3.
  • The Exit of the Program.

Below is the implementation:

# Give the number N as user input using int(input()) and store it in a variable.
numb = int(input('Enter some random number = '))
# Take a variable temp1 and initialize it to 1.
temp1 = 1
# Take another variable temp2 and initialize it to 2.
temp2 = 2
# Take the third variable temp3 and initialize it to 0.
temp3 = 0
# Now, print the first two numbers in the series,
# and we'll print the other generated numbers in the order they were generated.
print('The first', numb, 'numbers of the pell series are :')
print(temp1, temp2, end=' ')
# Loop till number -2 using For loop.
for i in range(numb-2):
    # Add the value of temp1 and twice the temp2 value
    # and initialize the temp3 with this value.
    temp3 = temp1+2*temp2
    # Swap the previous number for the previous number's predecessor (temp1 =temp2).
    temp1 = temp2
    # Swap the generated and previously generated numbers (temp2 = temp3)
    temp2 = temp3
    # Print the value of temp3.
    print(temp3, end=' ')

Output:

Enter some random number = 12
The first 12 numbers of the pell series are :
1 2 5 12 29 70 169 408 985 2378 5741 13860

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