nth_degree_direct_fibonacci_formulae.py

from typing import *
import numpy as np

def generate_fibonacci_function(degree: int, starting_values: List[int]):
    
    solutions = np.roots([1, *([-1]*degree)])
    
    def gen_coefficents(n):
        return [s**n for s in solutions]

    constants = np.linalg.solve([gen_coefficents(n) for n in range(degree)], starting_values)

    def direct_function(n):
        return round(sum([ c*s**n for c, s in zip(constants, solutions)]))
    
    return direct_function

print(generate_fibonacci_function(2, [1, 1])(20))