https://en.formulasearchengine.com/api.php?action=feedcontributions&feedformat=atom&user=103.245.12.2formulasearchengine - User contributions [en]2026-05-08T14:17:54ZUser contributionsMediaWiki 1.43.0-wmf.28https://en.formulasearchengine.com/index.php?title=Homology_sphere&diff=5695Homology sphere2013-06-19T08:28:55Z<p>103.245.12.2: /* Cosmology */</p>
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<div>In mathematics, a '''heptagonal pyramidal number''' is a [[figurate number]] representing the number of dots in a three-dimensional pattern in the shape of a [[heptagon]]al [[pyramid]].<ref name="dd">{{citation|title=Figurate Numbers|first1=Elena|last1=Deza|first2=M.|last2=Deza|author2-link=Michel Deza|publisher=World Scientific|year=2012|isbn=9789814355483|page=92|url=http://books.google.com/books?id=cDxYdstLPz4C&pg=PA92}}.</ref><br />
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The first few heptagonal pyramidal numbers are:<ref name="b">{{citation|title=Recreations in the Theory of Numbers: The Queen of Mathematics Entertains|first=Albert H.|last=Beiler|publisher=Courier Dover Publications|year=1966|isbn=9780486210964|page=194|url=http://books.google.com/books?id=fJTifbYNOzUC&pg=PA194}}.</ref><br />
:[[1 (number)|1]], [[8 (number)|8]], [[26 (number)|26]], [[60 (number)|60]], [[115 (number)|115]], 196, 308, 456, 645, 880, 1166, 1508, 1911, ... {{OEIS|id=A002413}}<br />
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The ''n''th heptagonal number can be calculated by adding up the first ''n'' [[heptagonal number]]s, or more directly by using the formula<ref name="dd"/><ref name="b"/><br />
:<math>\frac{n(n+1))5n-2)}{6}.</math><br />
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==References==<br />
{{reflist}}<br />
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{{Classes of natural numbers}}<br />
{{Num-stub}}<br />
[[Category:Figurate numbers]]</div>103.245.12.2