Editing Octahedral number (section)

{{short description|Number of close-packed spheres in an octahedron}}
[[File:Octahedral number.jpg|thumb|146 [[Neodymium magnet toys|magnetic balls]], packed in the form of an octahedron]]

In [[number theory]], an '''octahedral number''' is a [[figurate number]] that represents the number of spheres in an [[octahedron]] formed from [[close-packed spheres]]. The {{mvar|n}}th octahedral number <math>O_n</math> can be obtained by the formula:<ref name="bon">{{citation|title=The Book of Numbers|first1=John Horton|last1=Conway|author1-link=John Horton Conway|first2=Richard K.|last2=Guy|author2-link=Richard K. Guy|publisher=Springer-Verlag|year=1996|isbn=978-0-387-97993-9|page=50}}.</ref>

:<math>O_n={n(2n^2 + 1) \over 3}.</math>

The first few octahedral numbers are: 

:[[1 (number)|1]], [[6 (number)|6]], [[19 (number)|19]], [[44 (number)|44]], [[85 (number)|85]], 146, 231, 344, 489, 670, 891 {{OEIS|id=A005900}}.