maths.pell_number
=================

.. py:module:: maths.pell_number


Functions
---------

.. autoapisummary::

   maths.pell_number.pell_number_iterative
   maths.pell_number.pell_number_recursive


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

.. py:function:: pell_number_iterative(subscript: int) -> int

   This function returns the `subscript`-th Pell number iteratively, where
   `subscript` is a non-negative integer. Pell numbers are defined by the
   recurrence relation:

   P_0 = 0, P_1 = 1, P_n = 2 * P_(n-1) + P_(n-2)

   https://en.wikipedia.org/wiki/Pell_number
   https://oeis.org/A000129

   >>> pell_number_iterative(0)
   0
   >>> pell_number_iterative(1)
   1
   >>> pell_number_iterative(12)
   13860
   >>> pell_number_iterative("1")
   Traceback (most recent call last):
       ...
   ValueError: The input must be an integer.
   >>> pell_number_iterative(-1)
   Traceback (most recent call last):
       ...
   ValueError: The input number must be non-negative.


.. py:function:: pell_number_recursive(subscript: int) -> int

   This function calculates the `subscript`-th Pell number recursively. Due to
   its recursive nature, this function grows exponentially with `subscript`.
   For large values of `subscript`, use pell_number_iterative instead.

   >>> pell_number_recursive(0)
   0
   >>> pell_number_recursive(1)
   1
   >>> pell_number_recursive(12)
   13860
   >>> pell_number_recursive("1")
   Traceback (most recent call last):
       ...
   ValueError: The input must be an integer.
   >>> pell_number_recursive(-1)
   Traceback (most recent call last):
       ...
   ValueError: The input number must be non-negative.