@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-KGG4SL29-W
  skos:prefLabel "centered pentagonal number"@en, "nombre pentagonal centré"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Centered_pentagonal_number>, <https://fr.wikipedia.org/wiki/Nombre_pentagonal_centr%C3%A9> ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """En mathématiques, un nombre pentagonal centré est un nombre figuré polygonal centré qui peut être représenté par un pentagone régulier ayant un point placé en son centre et tous ses autres points disposés autour de ce centre en couches pentagonales successives de 5 points, 10 points, 15 points, etc. Ainsi, le n-ième pentagone centré comporte n points sur chaque rayon et sur chaque côté. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_pentagonal_centr%C3%A9">https://fr.wikipedia.org/wiki/Nombre_pentagonal_centr%C3%A9</a>)"""@fr, """A <b>centered pentagonal number</b> is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for <i>n</i> is given by the formula   <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle P_{n}={{5n^{2}-5n+2} \\\\over 2},n\\\\geq 1}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>P</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msub>         <mo>=</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow class="MJX-TeXAtom-ORD">               <mn>5</mn>               <msup>                 <mi>n</mi>                 <mrow class="MJX-TeXAtom-ORD">                   <mn>2</mn>                 </mrow>               </msup>               <mo>−<!-- − --></mo>               <mn>5</mn>               <mi>n</mi>               <mo>+</mo>               <mn>2</mn>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>,</mo>         <mi>n</mi>         <mo>≥<!-- ≥ --></mo>         <mn>1</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle P_{n}={{5n^{2}-5n+2} \\\\over 2},n\\\\geq 1}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21727ec6765cb11ed717291ef6a80948ffae9fdb" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:26.347ex; height:5.676ex;" alt="{\\\\displaystyle P_{n}={{5n^{2}-5n+2} \\\\over 2},n\\\\geq 1}"></span></dd></dl> The first few centered pentagonal numbers are 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601, 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 (sequence A005891 in the OEIS).  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Centered_pentagonal_number">https://en.wikipedia.org/wiki/Centered_pentagonal_number</a>)"""@en ;
  skos:broader psr:-XRXLKWR1-J ;
  a skos:Concept ;
  skos:inScheme psr: .

psr:-XRXLKWR1-J
  skos:prefLabel "nombre polygonal centré"@fr, "centered polygonal numbers"@en ;
  a skos:Concept ;
  skos:narrower psr:-KGG4SL29-W .