Iteration for Recurrent Problem with Python

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I am asked to find the 30th of a recurrence series, following the equation x(n) = 2*x(n-1) - x(n-2) for n >= 3, and x(1) = 0 and x(2) = 1.

Following the logic of fibonacci iteration, I have come up with the following code:

def loop(n):
    a = 0
    b = 1
    for i in range(30):
        a, b = b, 2 * b - a
    return a

Suiting in loop(30), I am returned 30, but I know mathematically that the answer should be 29. The code seems to be going one step ahead. Can anyone help point out what is incorrect in my code?

iteration python
2 Answers

You should only run the loop n - 1 times. Because the assignment a = 0 initializes x1. Then after each loop, a is assigned by the next value (from x2)

def loop(n):
    a = 0
    b = 1
    for i in range(n - 1):
        a, b = b, 2*b - a
    return a
    
print(loop(30))
# 29
user_147910200

You can notice that for the first time value of a=1 ( a=b=1;), According to the condition value of a is incremented by 1 ( a=b when b=2*b-1) so the output will be n on next nth iterations.;

user_119537420
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