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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Octahedral number ： ウィキペディア英語版 Octahedral number 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 ''n''th octahedral number $O\_n$ can be obtained by the formula:〔.〕 :$O\_n=.$ The first few octahedral numbers are: :1, 6, 19, 44, 85, 146, 231, 344, 489, 670, 891 . ==Properties and applications== The octahedral numbers have a generating function :$\backslash frac\; =\; \backslash sum\_^\; O\_n\; z^n\; =\; z\; +6z^2\; +\; 19z^3\; +\; \backslash cdots\; .$ Sir Frederick Pollock conjectured in 1850 that every number is the sum of at most 7 octahedral numbers: see Pollock octahedral numbers conjecture.〔.〕 In chemistry, octahedral numbers may be used to describe the numbers of atoms in octahedral clusters; in this context they are called magic numbers.〔.〕〔.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Octahedral number」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.