Hexagonal number sequence

maths/series/hexagonalnumbers.py

@@ -0,0 +1,98 @@
+# hexagonalnumbers.py
+
+"""
+A hexagonal number seqeunce 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.
+
+1. Calculates the hexagonal numbers sequence with a formula
+    hₙ = n(2n-1)
+    where:
+    hₙ --> is nth element of the sequence
+    n --> is the number of element in the sequence
+    reference-->"Hexagonal number" Wikipedia
+    <https://en.wikipedia.org/wiki/Hexagonal_number>
+
+2. Checks if a number is a hexagonal number with a formula
+    n = (sqrt(8x+1)+1)/4
+    where:
+    x --> is the number to check
+    n --> is a integer if x is a hexagonal number
+
+    reference-->"Hexagonal number" Wikipedia
+    <https://en.wikipedia.org/wiki/Hexagonal_number>
+"""
+
+
+class Error(Exception):
+    """Base class for other exceptions"""
+
+
+class ValueLessThanZero(Error):
+    """Raised when the input value is less than zero"""
+
+
+class ValueIsZero(Error):
+    """Raised when the input value is zero"""
+
+
+def len_check(len):
+    if len < 0:
+        raise ValueLessThanZero
+    elif len == 0:
+        raise ValueIsZero
+
+
+def hexagonal_numbers(len: int):
+    """
+    :param len: max number of elements
+    :type len: int
+    :return: Hexagonal numbers as a list
+
+    Tests:
+    >>> hexagonal_numbers(10)
+    [0, 1, 6, 15, 28, 45, 66, 91, 120, 153]
+    >>> hexagonal_numbers(5)
+    [0, 1, 6, 15, 28]
+    """
+
+    len_check(len)
+    hexagonal_numbers_list = []
+    for n in range(len):
+        num = n * (2 * n - 1)
+        hexagonal_numbers_list.append(num)
+    return hexagonal_numbers_list
+
+
+def check_if_hexagonal_number(num: int):
+    """
+    :param num: number to check
+    :type num: int
+    :return: boolean
+
+    Tests:
+    >>> check_if_hexagonal_number(120)
+    True
+    >>> check_if_hexagonal_number(5)
+    False
+    """
+
+    n = (((8 * num + 1) ** 1 / 2) + 1) / 4
+    isInt = True
+    try:
+        int(n)
+    except ValueError:
+        isInt = False
+    return isInt
+
+
+if __name__ == "__main__":
+    len = 5
+    hexagonal_numbers_list = hexagonal_numbers(len)
+    print(hexagonal_numbers_list)
+
+    num = 120
+    check = check_if_hexagonal_number(num)
+    print(check)