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Python program to find the solution of a special sum series

Here, we are going to learn how to find the solution of a given special sum series in Python? By Anuj Singh Last updated : January 04, 2024

Problem statement

We are going to design a special sum series function which has following characteristics:

f(0) = 0
f(1) = 1
f(2) = 1
f(3) = 0
f(x) = f(x-1) + f(x-3)

Python program to find the solution of a special sum series

# function to find the sum of the series
def summ(x):
    if x == 0:
        return 0
    if x == 1:
        return 1
    if x == 2:
        return 1
    if x == 3:
        return 0
    
    else:
        return summ(x-1) + summ(x-4)

# main code
if __name__ == '__main__':
    # finding the sum of the series till given value of x
    print("summ(0) :", summ(0))
    print("summ(1) :", summ(1))
    print("summ(2) :", summ(2))
    print("summ(3) :", summ(3))
    print("summ(10):", summ(10))
    print("summ(14):", summ(14))

Output

The output of the above example is:

summ(0) : 0
summ(1) : 1
summ(2) : 1
summ(3) : 0
summ(10): 5
summ(14): 17

To understand the above program, you should have the basic knowledge of the following Python topics:

• Python Variables
• Python Data Types
• Python print() Method
• Python Functions
• Python Conditional Statements

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