Euler's pentagonal formula

penta.py

"""Euler's pentagonal formula, by Cees Timmerman, 2020-11-23.
https://www.youtube.com/watch?v=iJ8pnCO0nTY"""
import math

def get_lookback_index(x: int):
    i = 0
    a = 0
    b = 1
    steps = [1]
    while i < x-1:
        i += 1
        if i % 2:
            a += 1
            steps.append(a)
        else:
            b += 2
            steps.append(b)

    return sum(steps)

def get_lookback_indexes(x: int):
    results = []
    i = 1
    while True:
        index = get_lookback_index(i)
        if index >= x: break
        results.append(index)
        i += 1

    return results

def euler_pentagonal_number(x: int):
    """
    >>> euler_pentagonal_number(0)
    1
    >>> euler_pentagonal_number(1)
    1
    >>> euler_pentagonal_number(666)
    11956824258286445517629485
    """
    result = 1
    numbers = [1, 1]
    for i in range(3, x+2):
        result = 0
        looks = get_lookback_indexes(i)
        #print(f"{i}th: {looks}")
        for count, look in enumerate(looks):
            factor = numbers[-look]
            if count % 4 > 1: factor *= -1
            #print("factor", factor)
            result += factor

        #print(f"Number {i-1} is {result:}")
        numbers.append(result)

    return result
    
print("{:,}".format(euler_pentagonal_number(666)))