Add leonardo numbers algorithm

maths/leonardo_numbers.py

@@ -0,0 +1,51 @@
+"""
+Leonardo numbers are a sequence of numbers given by the recurrence:
+L(n) = L(n-1) + L(n-2) + 1
+with initial values L(0) = 1 and L(1) = 1.
+
+Reference: https://en.wikipedia.org/wiki/Leonardo_number
+"""
+
+
+def leonardo_numbers(n: int) -> int:
+    """
+    Return the n-th Leonardo number.
+
+    >>> leonardo_numbers(0)
+    1
+    >>> leonardo_numbers(1)
+    1
+    >>> leonardo_numbers(2)
+    3
+    >>> leonardo_numbers(3)
+    5
+    >>> leonardo_numbers(4)
+    9
+    >>> leonardo_numbers(20)
+    21891
+    >>> leonardo_numbers(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be a non-negative integer
+    >>> leonardo_numbers(1.5)
+    Traceback (most recent call last):
+        ...
+    ValueError: n must be a non-negative integer
+    """
+    if not isinstance(n, int) or n < 0:
+        raise ValueError("n must be a non-negative integer")
+
+    if n in (0, 1):
+        return 1
+
+    previous, current = 1, 1
+    for _ in range(n - 1):
+        previous, current = current, previous + current + 1
+
+    return current
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()