algorithm: Hexagonal number (#8003)

* feat: Add hexagonal number

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maths/hexagonal_number.py

@@ -0,0 +1,48 @@
+"""
+== 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()