maths.padovan_sequence
======================

.. py:module:: maths.padovan_sequence


Functions
---------

.. autoapisummary::

   maths.padovan_sequence.padovan_sequence


Module Contents
---------------

.. py:function:: 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.