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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 Lucas sequence ： ウィキペディア英語版 Lucas sequence In mathematics, the Lucas sequences ''U''''n''(''P'',''Q'') and ''V''''n''(''P'',''Q'') are certain integer sequences that satisfy the recurrence relation :''x''''n'' = ''P x''''n''−1 − ''Q x''''n''−2 where ''P'' and ''Q'' are fixed integers. Any other sequence satisfying this recurrence relation can be represented as a linear combination of the Lucas sequences ''U''''n''(''P'',''Q'') and ''V''''n''(''P'',''Q''). More generally, Lucas sequences ''U''''n''(''P'',''Q'') and ''V''''n''(''P'',''Q'') represent sequences of polynomials in ''P'' and ''Q'' with integer coefficients. Famous examples of Lucas sequences include the Fibonacci numbers, Mersenne numbers, Pell numbers, Lucas numbers, Jacobsthal numbers, and a superset of Fermat numbers. Lucas sequences are named after the French mathematician Édouard Lucas. == Recurrence relations == Given two integer parameters ''P'' and ''Q'', the Lucas sequences of the first kind ''U''''n''(''P'',''Q'') and of the second kind ''V''''n''(''P'',''Q'') are defined by the recurrence relations: :$U\_0(P,Q)=0,\; \backslash ,$ :$U\_1(P,Q)=1,\; \backslash ,$ :$U\_n(P,Q)=P\backslash cdot\; U\_(P,Q)-Q\backslash cdot\; U\_(P,Q)\; \backslash mboxn>1,\; \backslash ,$ and :$V\_0(P,Q)=2,\; \backslash ,$ :$V\_1(P,Q)=P,\; \backslash ,$ :$V\_n(P,Q)=P\backslash cdot\; V\_(P,Q)-Q\backslash cdot\; V\_(P,Q)\; \backslash mboxn>1,\; \backslash ,$ It is not hard to show that for $n>0$, :$U\_n(P,Q)=\backslash frac(P,Q)\},\; \backslash ,$ :$V\_n(P,Q)=\backslash frac(P,Q)\}.\; \backslash ,$ 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「Lucas sequence」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.