Homology sphere: Difference between revisions

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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>
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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>
:[[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}}
 
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"/>
:<math>\frac{n(n+1))5n-2)}{6}.</math>
 
==References==
{{reflist}}
 
{{Classes of natural numbers}}
{{Num-stub}}
[[Category:Figurate numbers]]

Latest revision as of 00:27, 27 October 2014

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