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<main class="content quarto-banner-title-block" id="quarto-document-content"><section id="el-paquete-hexsticker" class="level2" data-number="1"><h2 data-number="1" data-anchor-id="el-paquete-hexsticker">
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<span class="header-section-number">1</span> El paquete <code>hexSticker</code>
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</h2>
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<p>El paquete <code>hexSticker</code> creado por <em>Guangchuang Yu</em> <span class="citation" data-cites="hexSticker"><a href="#ref-hexSticker" role="doc-biblioref">[1]</a></span> es una herramienta para generar <em>stickers</em> hexagonales reproducibles en R. Estos stickers son ideales como logos para paquetes de programación, blogs, proyectos o presentaciones. En este artículo post se muestra cómo crear el logo del la web <a href="https://www.energycode.org/">ENERGYCODE</a> usando una imagen extraída de un icono de un rayo blanco sobre un fondo negro, con ajustes para obtener el resultado deseado. Además, se soluciona el problema reportado en GitHub sobre que el borde hexagonal a veces se recorta al guardar en PNG o SVG (ver <a href="https://github.com/GuangchuangYu/hexSticker/issues/155?referrer=grok.com">issue #155</a>).</p>
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<p>El paquete <code>hexSticker</code> creado por <em>Guangchuang Yu</em> <span class="citation" data-cites="hexSticker">[<a href="#ref-hexSticker" role="doc-biblioref">1</a>]</span> es una herramienta para generar <em>stickers</em> hexagonales reproducibles en R. Estos stickers son ideales como logos para paquetes de programación, blogs, proyectos o presentaciones. En este artículo post se muestra cómo crear el logo del la web <a href="https://www.energycode.org/">ENERGYCODE</a> usando una imagen extraída de un icono de un rayo blanco sobre un fondo negro, con ajustes para obtener el resultado deseado. Además, se soluciona el problema reportado en GitHub sobre que el borde hexagonal a veces se recorta al guardar en PNG o SVG (ver <a href="https://github.com/GuangchuangYu/hexSticker/issues/155?referrer=grok.com">issue #155</a>).</p>
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<div class="cell">
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<details open="" class="code-fold"><summary>Código</summary><div class="sourceCode" id="cb1"><pre class="downlit sourceCode r code-with-copy"><code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://github.com/GuangchuangYu/hexSticker">hexSticker</a></span><span class="op">)</span></span>
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<span><span class="kw"><a href="https://rdrr.io/r/base/library.html">library</a></span><span class="op">(</span><span class="va"><a href="https://magrittr.tidyverse.org">magrittr</a></span><span class="op">)</span></span></code><button title="Copiar al portapapeles" class="code-copy-button"><i class="bi"></i></button></pre></div>
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</section><div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography" id="quarto-bibliography"><h2 class="anchored quarto-appendix-heading">
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6 Referencias</h2><div id="refs" class="references csl-bib-body" data-entry-spacing="0" role="list">
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6 Referencias</h2><div id="refs" class="references csl-bib-body" role="list">
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<div id="ref-hexSticker" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[1] </div>
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<div class="csl-right-inline">G. Yu, <em>hexSticker: Create Hexagon Sticker in R</em>. 2025. Disponible en: <a href="https://CRAN.R-project.org/package=hexSticker">https://CRAN.R-project.org/package=hexSticker</a>
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<span class="smallcaps">Yu</span>, G. (2025). <em><a href="https://CRAN.R-project.org/package=hexSticker">hexSticker: Create Hexagon Sticker in R</a></em>.</div>
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</div></section></div></main><!-- /main --><!-- partials/_footer.html --><footer class="quarto-footer"><div class="quarto-footer-left">
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© 2024–2026 Enrique Pérez Herrero

_site/posts/05032022-max-determinant/index.html

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<h2 data-number="3" data-anchor-id="references"><span class="header-section-number">3</span> References</h2>
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<div class="csl-left-margin">[1] </div><div class="csl-right-inline">N. J. A. Sloane, <span>A051125: Table t(n,k) = max<span>n,k</span> read by antidiagonals (n &gt;= 1, k &gt;= 1).</span> Available: <a href="https://oeis.org/A051125/">https://oeis.org/A051125/</a></div>
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<div class="csl-left-margin">[1] </div><div class="csl-right-inline"><span class="smallcaps">Sloane</span>, N. J. A. <a href="https://oeis.org/A051125/">A051125: Table t(n,k) = max<span>n,k</span> read by antidiagonals (n &gt;= 1, k &gt;= 1).</a> T. On-Line Encyclopedia of Integer Sequences, ed.</div>
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</div>
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<div id="ref-oeisA181983" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[2] </div><div class="csl-right-inline">M. Somos, <span>A181983: A(n) = (-1)^(n+1) * n.</span> 2012. Available: <a href="https://oeis.org/A181983/">https://oeis.org/A181983/</a></div>
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<div class="csl-left-margin">[2] </div><div class="csl-right-inline"><span class="smallcaps">Somos</span>, M. (2012). <a href="https://oeis.org/A181983/">A181983: A(n) = (-1)^(n+1) * n.</a> T. On-Line Encyclopedia of Integer Sequences, ed.</div>
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<div id="ref-oeisA161124" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[3] </div><div class="csl-right-inline">E. Deutsch, <span>A161124: Number of inversions in all fixed-point-free involutions of <span>1,2,...,2n</span>.</span> Jun. 2009. Available: <a href="https://oeis.org/A161124/">https://oeis.org/A161124/</a></div>
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<div class="csl-left-margin">[3] </div><div class="csl-right-inline"><span class="smallcaps">Deutsch</span>, E. (2009). <a href="https://oeis.org/A161124/">A161124: Number of inversions in all fixed-point-free involutions of <span>1,2,...,2n</span>.</a> T. On-Line Encyclopedia of Integer Sequences, ed.</div>
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<div id="ref-oeisA001147" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[4] </div><div class="csl-right-inline">N. J. A. Sloane, <span>A001147: Double factorial of odd numbers: A(n) = (2*n-1)!! = 1*3*5*...*(2*n-1).</span> Available: <a href="https://oeis.org/A001147/">https://oeis.org/A001147/</a></div>
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<div class="csl-left-margin">[4] </div><div class="csl-right-inline"><span class="smallcaps">Sloane</span>, N. J. A. <a href="https://oeis.org/A001147/">A001147: Double factorial of odd numbers: A(n) = (2*n-1)!! = 1*3*5*...*(2*n-1).</a> T. On-Line Encyclopedia of Integer Sequences, ed.</div>
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_site/posts/08012026-suma-reciprocos-tetraedricos/index.html

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<h2 data-number="2" data-anchor-id="números-tetraédricos"><span class="header-section-number">2</span> NÚMEROS TETRAÉDRICOS</h2>
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<p>Los números tetraédricos representan el número de esferas que pueden apilarse formando un <em>tetraedro regular</em> <span class="citation" data-cites="wikiTetrahedralNumber"><a href="#ref-wikiTetrahedralNumber" role="doc-biblioref">[2]</a></span> <span class="citation" data-cites="mathworldTetrahedralNumber"><a href="#ref-mathworldTetrahedralNumber" role="doc-biblioref">[3]</a></span> y están definidos por la fórmula</p>
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<p>Los números tetraédricos representan el número de esferas que pueden apilarse formando un <em>tetraedro regular</em> <span class="citation" data-cites="wikiTetrahedralNumber">[<a href="#ref-wikiTetrahedralNumber" role="doc-biblioref">2</a>]</span> <span class="citation" data-cites="mathworldTetrahedralNumber">[<a href="#ref-mathworldTetrahedralNumber" role="doc-biblioref">3</a>]</span> y están definidos por la fórmula</p>
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<p><span id="eq-tet001"><span class="math display">
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T_n = \frac{n(n+1)(n+2)}{6} = \binom{n+2}{3}
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<h2 data-number="5" data-anchor-id="números-armónicos"><span class="header-section-number">5</span> NÚMEROS ARMÓNICOS</h2>
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<p>Estas tres series se pueden sumar facilmente teniendo en cuenta las siguientes identidades para los <em>números armónicos</em> <span class="math inline">H_n</span> <span class="citation" data-cites="wikiHarmonicNumber"><a href="#ref-wikiHarmonicNumber" role="doc-biblioref">[4]</a></span>:</p>
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<p>Estas tres series se pueden sumar facilmente teniendo en cuenta las siguientes identidades para los <em>números armónicos</em> <span class="math inline">H_n</span> <span class="citation" data-cites="wikiHarmonicNumber">[<a href="#ref-wikiHarmonicNumber" role="doc-biblioref">4</a>]</span>:</p>
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<div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography" id="quarto-bibliography"><h2 class="anchored quarto-appendix-heading">8 REFERENCIAS</h2><div id="refs" class="references csl-bib-body" data-entry-spacing="0" role="list">
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<div id="quarto-appendix" class="default"><section class="quarto-appendix-contents" role="doc-bibliography" id="quarto-bibliography"><h2 class="anchored quarto-appendix-heading">8 REFERENCIAS</h2><div id="refs" class="references csl-bib-body" role="list">
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<div id="ref-psychedelic2009" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[1] </div><div class="csl-right-inline">P. Geometry, <span>«TETRAHEDRAL NUMBERS RECIPROCALS SUM»</span>. 2009. Disponible en: <a href="https://psychedelicgeometry.wordpress.com/2009/12/25/tetrahedral-numbers-reciprocals-sum/">https://psychedelicgeometry.wordpress.com/2009/12/25/tetrahedral-numbers-reciprocals-sum/</a></div>
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<div class="csl-left-margin">[1] </div><div class="csl-right-inline"><span class="smallcaps">Geometry</span>, P. (2009). <a href="https://psychedelicgeometry.wordpress.com/2009/12/25/tetrahedral-numbers-reciprocals-sum/">TETRAHEDRAL NUMBERS RECIPROCALS SUM</a>.</div>
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<div id="ref-wikiTetrahedralNumber" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[2] </div><div class="csl-right-inline"><span>«Tetrahedral number»</span>. Wikipedia; <a href="https://en.wikipedia.org/wiki/Tetrahedral_number" class="uri">https://en.wikipedia.org/wiki/Tetrahedral_number</a>.</div>
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<div class="csl-left-margin">[2] </div><div class="csl-right-inline"><span class="smallcaps">Anón</span>. Tetrahedral number.</div>
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<div id="ref-mathworldTetrahedralNumber" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[3] </div><div class="csl-right-inline">E. W. Weisstein, <span>«Tetrahedral Number»</span>. From MathWorld–A Wolfram Web Resource. Disponible en: <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">http://mathworld.wolfram.com/TetrahedralNumber.html</a></div>
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<div class="csl-left-margin">[3] </div><div class="csl-right-inline"><span class="smallcaps">Weisstein</span>, E. W. <a href="http://mathworld.wolfram.com/TetrahedralNumber.html">Tetrahedral Number</a>.</div>
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<div id="ref-wikiHarmonicNumber" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[4] </div><div class="csl-right-inline"><span>«Harmonic number»</span>. Wikipedia; <a href="https://en.wikipedia.org/wiki/Harmonic_number" class="uri">https://en.wikipedia.org/wiki/Harmonic_number</a>.</div>
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<div class="csl-left-margin">[4] </div><div class="csl-right-inline"><span class="smallcaps">Anón</span>. Harmonic number.</div>
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<div id="ref-oeisA000292" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[5] </div><div class="csl-right-inline">Online Encyclopedia of Integer Sequences, <span>«Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6</span> <a href="https://oeis.org/A000292" class="uri">https://oeis.org/A000292</a>, 2009.</div>
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<div class="csl-left-margin">[5] </div><div class="csl-right-inline"><span class="smallcaps">Online Encyclopedia of Integer Sequences</span>. (2009). Tetrahedral (or triangular pyramidal) numbers: a(n) = C(n+2,3) = n*(n+1)*(n+2)/6.</div>
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<div id="ref-caglayan2015" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[6] </div><div class="csl-right-inline">G. Caglayan, <span>«Proof Without Words: Series of Reciprocals of Tetrahedral Numbers»</span>, <em>The College Mathematics Journal</em>, vol. 46, n.º 2, p. 130, 2015, doi: <a href="https://doi.org/10.4169/college.math.j.46.2.130">10.4169/college.math.j.46.2.130</a>.</div>
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<div class="csl-left-margin">[6] </div><div class="csl-right-inline"><span class="smallcaps">Caglayan</span>, G. (2015). <a href="https://doi.org/10.4169/college.math.j.46.2.130">Proof Without Words: Series of Reciprocals of Tetrahedral Numbers</a>. <em>The College Mathematics Journal</em> <strong>46</strong> 130.</div>
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<div id="ref-oeisA118391" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[7] </div><div class="csl-right-inline">J. V. Post, A. Adamchuk, G. C. Greubel, H. P. Dale, y P. Carmody, <span>«A118391: Numerator of sum of reciprocals of first n tetrahedral numbers»</span>. <a href="https://oeis.org/A118391" class="uri">https://oeis.org/A118391</a>, 2006.</div>
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<div class="csl-left-margin">[7] </div><div class="csl-right-inline"><span class="smallcaps">Post</span>, J. V., <span class="smallcaps">Adamchuk</span>, A., <span class="smallcaps">Greubel</span>, G. C., <span class="smallcaps">Dale</span>, H. P. y <span class="smallcaps">Carmody</span>, P. (2006). A118391: Numerator of sum of reciprocals of first n tetrahedral numbers.</div>
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<div id="ref-oeisA118392" class="csl-entry" role="listitem">
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<div class="csl-left-margin">[8] </div><div class="csl-right-inline">J. V. Post, H. P. Dale, y G. C. Greubel, <span>«A118392: Denominator of sum of reciprocals of first n tetrahedral numbers»</span>. <a href="https://oeis.org/A118392" class="uri">https://oeis.org/A118392</a>, 2006.</div>
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<div class="csl-left-margin">[8] </div><div class="csl-right-inline"><span class="smallcaps">Post</span>, J. V., <span class="smallcaps">Dale</span>, H. P. y <span class="smallcaps">Greubel</span>, G. C. (2006). A118392: Denominator of sum of reciprocals of first n tetrahedral numbers.</div>
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</div></section><section id="footnotes" class="footnotes footnotes-end-of-document" role="doc-endnotes"><h2 class="anchored quarto-appendix-heading">Notas</h2>
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<li id="fn1"><p>Este artículo es una <em>traducción y actualización</em> del post original titulado <em>TETRAHEDRAL NUMBERS RECIPROCALS SUM</em> publicado el <em>viernes 25 de diciembre de 2009</em> en el blog <em>Psychedelic Geometry</em> <span class="citation" data-cites="psychedelic2009"><a href="#ref-psychedelic2009" role="doc-biblioref">[1]</a></span>.<a href="#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
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<li id="fn1"><p>Este artículo es una <em>traducción y actualización</em> del post original titulado <em>TETRAHEDRAL NUMBERS RECIPROCALS SUM</em> publicado el <em>viernes 25 de diciembre de 2009</em> en el blog <em>Psychedelic Geometry</em> <span class="citation" data-cites="psychedelic2009">[<a href="#ref-psychedelic2009" role="doc-biblioref">1</a>]</span>.<a href="#fnref1" class="footnote-back" role="doc-backlink">↩︎</a></p></li>
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