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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 Alcuin's sequence ： ウィキペディア英語版 Alcuin's sequence In mathematics, Alcuin's sequence, named after Alcuin of York, is the sequence of coefficients of the power-series expansion of: : $\backslash frac\; =\; x^3\; +\; x^5\; +\; x^6\; +\; 2x^7\; +\; x^8\; +\; 3x^9\; +\; \backslash cdots.$ The sequence begins with these integers:〔 : 0, 0, 0, 1, 0, 1, 1, 2, 1, 3, 2, 4, 3, 5, 4, 7, 5, 8, 7, 10, 8, 12, 10, 14, 12, 16, 14, 19, 16, 21 The ''n''th term is the number of triangles with integer sides and perimeter ''n''.〔 It is also the number of triangles with ''distinct'' integer sides and perimeter ''n'' + 6, i.e. number of triples (''a'', ''b'', ''c'') such that 1 ≤ ''a'' < ''b'' < ''c'' < ''a'' + ''b'', ''a'' + ''b'' + ''c'' = ''n'' + 6. If one deletes the three leading zeros, then it is the number of ways in which ''n'' empty casks, ''n'' casks half-full of wine and ''n'' full casks can be distributed to three persons in such a way that each one gets the same number of casks and the same amount of wine. ==References== 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「Alcuin's 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.