Sharing answer codes of mine about HackerRank: Fibonacci Modified.

# HackerRank: Fibonacci Modified (in Algorithm)

## Problem Statement

We define a *modified Fibonacci sequence* using the following definition:

Given terms \(t_i\) and \(t_{i+1}\) where \(i \in [1,\infty)\), term \(t_{i+2}\) is computed using the following relation:

For example, if term \(t_1 =0\) and \(t_2 =1\), term \(t_3 = 0 + 1^2 = 1\), term \(t_4 = 1 + 1^2 = 2\), term \(t_5 = 1 + 2^2 = 5\), and so on.

Given three integers, \(t_1\), \(t_2\), and \(n\), compute and print term \(t_n\) of a modified Fibonacci sequence.

Note: The value of \(t_n\) may far exceed the range of a 64-bit integer. Many submission languages have libraries that can handle such large results but, for those that don’t (e.g., C++), you will need to be more creative in your solution to compensate for the limitations of your chosen submission language.

## Answer Code (in Python3)

- Time complexity: \(O(n)\)

```
#!/bin/python3
import sys
def fibonacciModified(t1, t2, n):
# t_{i+2}=t_{i}+(t_{i+1})^2
lookup=[t1, t2]
for i in range(2, n):
lookup.append(lookup[i-2] + (lookup[i-1]*lookup[i-1]))
return lookup[n-1]
if __name__ == "__main__":
t1, t2, n = input().strip().split(' ')
t1, t2, n = [int(t1), int(t2), int(n)]
result = fibonacciModified(t1, t2, n)
print(result)
```