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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 Centered cube number ： ウィキペディア英語版 Centered cube number A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with ''i''2 points on the square faces of the ''i''th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has ''n'' + 1 points along each of its edges. The first few centered cube numbers are :1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, ... . ==Formulas== The centered cube number for a pattern with ''n'' concentric layers around the central point is given by the formula〔.〕 :$n^3\; +\; (n\; +\; 1)^3\; =\; (2n+1)(n^2+n+1).$ The same number can also be expressed as a trapezoidal number (difference of two triangular numbers), or a sum of consecutive numbers, as〔.〕 :$\backslash binom-\backslash binom\; =\; (n^2+1)+(n^2+2)+\backslash cdots+(n+1)^2.$ 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「Centered cube 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.