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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 Jacobsthal number ： ウィキペディア英語版 Jacobsthal number In mathematics, the Jacobsthal numbers are an integer sequence named after the German mathematician Ernst Jacobsthal. Like the related Fibonacci numbers, they are a specific type of Lucas sequence $U\_n(P,Q)$ for which ''P'' = 1, and ''Q'' = −2—and are defined by a similar recurrence relation: in simple terms, the sequence starts with 0 and 1, then each following number is found by adding the number before it to twice the number before that. The first Jacobsthal numbers are: :0, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, … == Jacobsthal numbers == Jacobsthal numbers are defined by the recurrence relation: :$$ J_n = \begin 0 & \mbox n = 0; \\ 1 & \mbox n = 1; \\ J_ + 2J_ & \mbox n > 1. \\ \end The next Jacobsthal number is also given by the recursion formula: : $J\_\; =\; 2J\_n\; +\; (-1)^n\; \backslash ,\; ,$ or by: : $J\_\; =\; 2^n\; -\; J\_n.\; \backslash ,$ The first recursion formula above is also satisfied by the powers of 2. The Jacobsthal number at a specific point in the sequence may be calculated directly using the closed-form equation: :$$ J_n = \frac 3. The generating function for the Jacobsthal numbers is :$\backslash frac.$ 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「Jacobsthal 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.