Python/maths/hexagonal_number.py

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"""
== Hexagonal Number ==
The nth hexagonal number hn is the number of distinct dots
in a pattern of dots consisting of the outlines of regular
hexagons with sides up to n dots, when the hexagons are
overlaid so that they share one vertex.
https://en.wikipedia.org/wiki/Hexagonal_number
"""
# Author : Akshay Dubey (https://github.com/itsAkshayDubey)
def hexagonal(number: int) -> int:
"""
:param number: nth hexagonal number to calculate
:return: the nth hexagonal number
Note: A hexagonal number is only defined for positive integers
>>> hexagonal(4)
28
>>> hexagonal(11)
231
>>> hexagonal(22)
946
>>> hexagonal(0)
Traceback (most recent call last):
...
ValueError: Input must be a positive integer
>>> hexagonal(-1)
Traceback (most recent call last):
...
ValueError: Input must be a positive integer
>>> hexagonal(11.0)
Traceback (most recent call last):
...
TypeError: Input value of [number=11.0] must be an integer
"""
if not isinstance(number, int):
raise TypeError(f"Input value of [number={number}] must be an integer")
if number < 1:
raise ValueError("Input must be a positive integer")
return number * (2 * number - 1)
if __name__ == "__main__":
import doctest
doctest.testmod()