.. _sphx_glr_api_gallery_combinatorics_sequences:

Integer sequences
-----------------

Fibonacci numbers, Bernoulli numbers and sums of powers, and Gray
codes.


.. raw:: html

  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


.. raw:: html

    <div class="sphx-glr-thumbnails">

.. thumbnail-parent-div-open

.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Reproduces the rabbit problem from Fibonacci&#x27;s 1202 Liber Abaci, checks that the same numbers count domino tilings of a 2-by-n strip, and shows the ratio of successive terms approaching the golden ratio.">

.. only:: html

  .. image:: /api/gallery/combinatorics/sequences/images/thumb/sphx_glr_plot_01_fibonacci_rabbits_thumb.png
    :alt:

  :doc:`/api/gallery/combinatorics/sequences/plot_01_fibonacci_rabbits`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Fibonacci's rabbits and domino tilings</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Computes the Bernoulli numbers exactly, uses them to evaluate sums of p-th powers in closed form, and repeats Bernoulli&#x27;s own boast: the sum of the tenth powers of the first 1000 integers.">

.. only:: html

  .. image:: /api/gallery/combinatorics/sequences/images/thumb/sphx_glr_plot_02_bernoulli_power_sums_thumb.png
    :alt:

  :doc:`/api/gallery/combinatorics/sequences/plot_02_bernoulli_power_sums`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Jacob Bernoulli's numbers and sums of powers</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Lists the reflected binary Gray code, checks that neighbouring codes differ in exactly one bit, and compares the number of bit flips needed to count through all n-bit words with ordinary binary counting.">

.. only:: html

  .. image:: /api/gallery/combinatorics/sequences/images/thumb/sphx_glr_plot_03_gray_code_thumb.png
    :alt:

  :doc:`/api/gallery/combinatorics/sequences/plot_03_gray_code`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">Gray codes: counting one bit at a time</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:

   /api/gallery/combinatorics/sequences/plot_01_fibonacci_rabbits
   /api/gallery/combinatorics/sequences/plot_02_bernoulli_power_sums
   /api/gallery/combinatorics/sequences/plot_03_gray_code