From a0a7ca0267df72daab0c79ae6055b447eb1500ce Mon Sep 17 00:00:00 2001
From: Prakriti Manhar <prakritim01@users.noreply.github.com>
Date: Fri, 12 Dec 2025 13:37:30 +0530
Subject: [PATCH 1/2] Add Padovan Sequence algorithm in maths

---
 maths/padovan_sequence.py | 48 +++++++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 maths/padovan_sequence.py

diff --git a/maths/padovan_sequence.py b/maths/padovan_sequence.py
new file mode 100644
index 000000000000..accbb341fbad
--- /dev/null
+++ b/maths/padovan_sequence.py
@@ -0,0 +1,48 @@
+def padovan_sequence(n: int) -> int:
+    """
+    Return the n-th term of the Padovan Sequence.
+    The Padovan sequence is the sequence of integers P(n) defined by the initial values
+    P(0) = P(1) = P(2) = 1 and the recurrence relation P(n) = P(n-2) + P(n-3).
+
+    https://en.wikipedia.org/wiki/Padovan_sequence
+
+    :param n: The index of the term to return.
+    :return: The n-th term of the Padovan Sequence.
+
+    >>> padovan_sequence(0)
+    1
+    >>> padovan_sequence(1)
+    1
+    >>> padovan_sequence(2)
+    1
+    >>> padovan_sequence(3)
+    2
+    >>> padovan_sequence(4)
+    2
+    >>> padovan_sequence(5)
+    3
+    >>> padovan_sequence(10)
+    12
+    >>> padovan_sequence(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Input must be a non-negative integer.
+    """
+    if not isinstance(n, int) or n < 0:
+        raise ValueError("Input must be a non-negative integer.")
+
+    if n <= 2:
+        return 1
+
+    p_prev_3, p_prev_2, p_prev_1 = 1, 1, 1
+
+    for _ in range(3, n + 1):
+        curr = p_prev_2 + p_prev_3
+        p_prev_3, p_prev_2, p_prev_1 = p_prev_2, p_prev_1, curr
+
+    return p_prev_1
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
+    print("Doctests passed!")

From f022d1e84ae1a93042921ba919b0a8e67a984d04 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Fri, 12 Dec 2025 08:12:46 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/padovan_sequence.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/maths/padovan_sequence.py b/maths/padovan_sequence.py
index accbb341fbad..1ad756af2e28 100644
--- a/maths/padovan_sequence.py
+++ b/maths/padovan_sequence.py
@@ -42,7 +42,9 @@ def padovan_sequence(n: int) -> int:
 
     return p_prev_1
 
+
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()
     print("Doctests passed!")