<ulclass="metadata page-metadata"data-bi-name="page info"lang="en-us"dir="ltr">

Last update:

<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April 19, 202503:11:59">April 19, 2025</span>&emsp;

<spanclass="git-revision-date-localized-plugin git-revision-date-localized-plugin-date"title="April 19, 202507:56:55">April 19, 2025</span>&emsp;

\end{pmatrix}

$$</div>

<p>where<spanclass="arithmatex">$F_1 = 1, F_0 = 0$</span>.

In fact, since

$$

\begin{pmatrix} 1 &amp; 1 \ 1 &amp; 0 \end{pmatrix}

= \begin{pmatrix} F_2 &amp; F_1 \ F_1 &amp; F_0 \end{pmatrix}

$$</p>

In fact, since</p>

<divclass="arithmatex">$$

\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}

= \begin{pmatrix} F_2 &amp; F_1 \\ F_1 &amp; F_0 \end{pmatrix}

$$</div>

<p>we can use the matrix directly:</p>

<divclass="arithmatex">$$

\begin{pmatrix} 1 &amp; 1 \\ 1 &amp; 0 \end{pmatrix}^n

<ulclass="metadata page-metadata"data-bi-name="page info"lang="en-us"dir="ltr">

<spanclass="contributors-text">Contributors:</span>

<ulclass="contributors"data-bi-name="contributors"><li><ahref="https://github.com/gabrielsimoes"title="gabrielsimoes"data-bi-name="contributorprofile"target="_blank">gabrielsimoes</a> (23.79%)</li><li><ahref="https://github.com/jakobkogler"title="jakobkogler"data-bi-name="contributorprofile"target="_blank">jakobkogler</a> (20.69%)</li><li><ahref="https://github.com/jxu"title="jxu"data-bi-name="contributorprofile"target="_blank">jxu</a> (18.62%)</li><li><ahref="#"title="Carlos Javier Blanco"data-bi-name="contributorprofile"target="_blank">Carlos Javier Blanco</a> (15.86%)</li><li><ahref="https://github.com/madhur4127"title="madhur4127"data-bi-name="contributorprofile"target="_blank">madhur4127</a> (6.21%)</li><li><ahref="https://github.com/tcNickolas"title="tcNickolas"data-bi-name="contributorprofile"target="_blank">tcNickolas</a> (5.17%)</li><li><ahref="https://github.com/adamant-pwn"title="adamant-pwn"data-bi-name="contributorprofile"target="_blank">adamant-pwn</a> (2.4099999999999997%)</li><li><ahref="https://github.com/Morass"title="Morass"data-bi-name="contributorprofile"target="_blank">Morass</a> (2.07%)</li><li><ahref="https://github.com/md-shamim-ahmad"title="md-shamim-ahmad"data-bi-name="contributorprofile"target="_blank">md-shamim-ahmad</a> (1.72%)</li><li><ahref="https://github.com/boxlesscat"title="boxlesscat"data-bi-name="contributorprofile"target="_blank">boxlesscat</a> (1.03%)</li><li><ahref="https://github.com/yeetholmes619"title="yeetholmes619"data-bi-name="contributorprofile"target="_blank">yeetholmes619</a> (1.03%)</li><li><ahref="https://github.com/pasthec"title="pasthec"data-bi-name="contributorprofile"target="_blank">pasthec</a> (0.69%)</li><li><ahref="https://github.com/conlacda"title="conlacda"data-bi-name="contributorprofile"target="_blank">conlacda</a> (0.34%)</li><li><ahref="https://github.com/ankit-kumar-dwivedi"title="ankit-kumar-dwivedi"data-bi-name="contributorprofile"target="_blank">ankit-kumar-dwivedi</a> (0.34%)</li></ul>

<ulclass="contributors"data-bi-name="contributors"><li><ahref="https://github.com/gabrielsimoes"title="gabrielsimoes"data-bi-name="contributorprofile"target="_blank">gabrielsimoes</a> (23.71%)</li><li><ahref="https://github.com/jakobkogler"title="jakobkogler"data-bi-name="contributorprofile"target="_blank">jakobkogler</a> (20.62%)</li><li><ahref="https://github.com/jxu"title="jxu"data-bi-name="contributorprofile"target="_blank">jxu</a> (18.56%)</li><li><ahref="#"title="Carlos Javier Blanco"data-bi-name="contributorprofile"target="_blank">Carlos Javier Blanco</a> (15.81%)</li><li><ahref="https://github.com/madhur4127"title="madhur4127"data-bi-name="contributorprofile"target="_blank">madhur4127</a> (6.19%)</li><li><ahref="https://github.com/tcNickolas"title="tcNickolas"data-bi-name="contributorprofile"target="_blank">tcNickolas</a> (5.15%)</li><li><ahref="https://github.com/adamant-pwn"title="adamant-pwn"data-bi-name="contributorprofile"target="_blank">adamant-pwn</a> (2.75%)</li><li><ahref="https://github.com/Morass"title="Morass"data-bi-name="contributorprofile"target="_blank">Morass</a> (2.06%)</li><li><ahref="https://github.com/md-shamim-ahmad"title="md-shamim-ahmad"data-bi-name="contributorprofile"target="_blank">md-shamim-ahmad</a> (1.72%)</li><li><ahref="https://github.com/boxlesscat"title="boxlesscat"data-bi-name="contributorprofile"target="_blank">boxlesscat</a> (1.03%)</li><li><ahref="https://github.com/yeetholmes619"title="yeetholmes619"data-bi-name="contributorprofile"target="_blank">yeetholmes619</a> (1.03%)</li><li><ahref="https://github.com/pasthec"title="pasthec"data-bi-name="contributorprofile"target="_blank">pasthec</a> (0.69%)</li><li><ahref="https://github.com/conlacda"title="conlacda"data-bi-name="contributorprofile"target="_blank">conlacda</a> (0.34%)</li><li><ahref="https://github.com/ankit-kumar-dwivedi"title="ankit-kumar-dwivedi"data-bi-name="contributorprofile"target="_blank">ankit-kumar-dwivedi</a> (0.34%)</li></ul>