https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=2.96.95.0%2F24 2026-08-23T17:38:01Z User contributions MediaWiki 1.47.0-wmf.7 https://en.formulasearchengine.com/w/index.php?title=Cross-polytope&diff=6347 2013-09-12T10:13:41Z

<p>2.96.95.40: Tidy latex</p> <hr /> <div>{{refimprove|date=August 2012}}<br /> [[Image:Nombre pentagon cent.svg|240px|right]]<br /> <br /> A '''centered pentagonal number''' is a [[centered polygonal number|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 ''n'' is given by the formula <br /> <br /> :&lt;math&gt;{{5(n-1)^2 + 5(n-1) + 2} \over 2}.&lt;/math&gt;<br /> <br /> The first few centered pentagonal numbers are<br /> <br /> [[1 (number)|1]], [[6 (number)|6]], [[16 (number)|16]], [[31 (number)|31]], [[51 (number)|51]], [[76 (number)|76]], [[106 (number)|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 {{OEIS|A005891}}.<br /> <br /> The parity of centered pentagonal numbers follows the pattern even-even-odd-odd, and in base 10 the units follow the pattern <br /> 6-6-1-1.<br /> <br /> ==See also==<br /> *[[Pentagonal number]]<br /> *[[Polygonal number]]<br /> *[[Centered polygonal number]]<br /> <br /> ==External links==<br /> *{{mathworld|title=Centered pentagonal number|urlname=CenteredPentagonalNumber}}<br /> <br /> [[Category:Figurate numbers]]<br /> <br /> {{Classes of natural numbers}}<br /> <br /> {{num-stub}}</div>

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