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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 hexagonal number ： ウィキペディア英語版 Centered hexagonal number A centered hexagonal number, or hex number, is a centered figurate number that represents a hexagon with a dot in the center and all other dots surrounding the center dot in a hexagonal lattice. The th centered hexagonal number is given by the formula :$n^3\; -\; (n-1)^3\; =\; 3n(n-1)+1.\backslash ,$ Expressing the formula as :$1+6\backslash left(n(n-1)\backslash right)$ shows that the centered hexagonal number for is 1 more than 6 times the th triangular number. The first few centered hexagonal numbers are : :1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919. In base 10 one can notice that the hexagonal numbers' rightmost (least significant) digits follow the pattern 1–7–9–7–1. Centered hexagonal numbers have practical applications in materials logistics management, for example, in packing round items into larger round containers, such as Vienna sausages into round cans, or combining individual wire strands into a cable. The sum of the first centered hexagonal numbers happens to be . That is, centered hexagonal pyramidal numbers and cubes are the same numbers, but they represent different shapes. Viewed from the opposite perspective, centered hexagonal numbers are differences of two consecutive cubes, so that the centered hexagonal numbers are the gnomon of the cubes. In particular, prime centered hexagonal numbers are cuban primes. The difference between and the th centered hexagonal number is a number of the form , while the difference between and the th centered hexagonal number is a pronic number. ==See also== *Hexagonal number *Magic hexagon *Star number 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 hexagonal 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.