6 kyu Sum of a Sequence [Hard-Core Version].py

"""
https://www.codewars.com/kata/587a88a208236efe8500008b/train/python

As the title suggests, this is the hard-core version of another neat kata.

The task is simple to explain: simply sum all the numbers from the first parameter being the beginning to the second parameter being the upper limit (possibly included), going in steps expressed by the third parameter:

sequence_sum(2, 2, 2) # 2
sequence_sum(2, 6, 2) # 12 (= 2 + 4 + 6)
sequence_sum(1, 5, 1) # (= 1 + 2 + 3 + 4 + 5)
sequence_sum(1, 5, 3) # 5 (= 1 + 4)

If it is an impossible sequence (with the beginning being larger the end and a positive step or the other way around), just return 0. See the provided test cases for further examples :)

Note: differing from the other base kata, much larger ranges are going to be tested, so you should hope to get your algo optimized and to avoid brute-forcing your way through the solution.
"""


def sequence_sum(begin_number, end_number, step):
    if begin_number > end_number and step > 0 or begin_number < end_number and step < 0:
        return 0

    formula = (end_number - begin_number) // step + 1

    return (2 * begin_number + step * (formula - 1)) * formula // 2