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* Hexagonal number sequence A hexagonal number sequence is a sequence of figurate numbers where 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. This program returns the hexagonal number sequence of n length. * Update hexagonalnumbers.py * Update hexagonalnumbers.py * Update hexagonalnumbers.py * Update hexagonalnumbers.py * Update and rename hexagonalnumbers.py to hexagonal_numbers.py * Length must be a positive integer Co-authored-by: Christian Clauss <cclauss@me.com>
43 lines
1.3 KiB
Python
43 lines
1.3 KiB
Python
"""
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A hexagonal number sequence is a sequence of figurate numbers
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where the nth hexagonal number hₙ is the number of distinct dots
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in a pattern of dots consisting of the outlines of regular
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hexagons with sides up to n dots, when the hexagons are overlaid
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so that they share one vertex.
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Calculates the hexagonal numbers sequence with a formula
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hₙ = n(2n-1)
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where:
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hₙ --> is nth element of the sequence
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n --> is the number of element in the sequence
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reference-->"Hexagonal number" Wikipedia
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<https://en.wikipedia.org/wiki/Hexagonal_number>
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"""
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def hexagonal_numbers(length: int) -> list[int]:
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"""
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:param len: max number of elements
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:type len: int
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:return: Hexagonal numbers as a list
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Tests:
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>>> hexagonal_numbers(10)
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[0, 1, 6, 15, 28, 45, 66, 91, 120, 153]
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>>> hexagonal_numbers(5)
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[0, 1, 6, 15, 28]
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>>> hexagonal_numbers(0)
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Traceback (most recent call last):
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...
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ValueError: Length must be a positive integer.
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"""
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if length <= 0 or not isinstance(length, int):
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raise ValueError("Length must be a positive integer.")
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return [n * (2 * n - 1) for n in range(length)]
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if __name__ == "__main__":
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print(hexagonal_numbers(length=5))
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print(hexagonal_numbers(length=10))
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