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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 Delannoy number ： ウィキペディア英語版 Delannoy number In mathematics, a Delannoy number $D$ describes the number of paths from the southwest corner (0, 0) of a rectangular grid to the northeast corner (''m'', ''n''), using only single steps north, northeast, or east. The Delannoy numbers are named after French army officer and amateur mathematician Henri Delannoy. The Delannoy number $D(m,n)$ also counts the number of global alignments of two sequences of lengths $m$ and $n$, the number of points in an ''m''-dimensional integer lattice that are at most ''n'' steps from the origin, and, in cellular automata, the number of cells in an ''m''-dimensional von Neumann neighborhood of radius ''n''. ==Example== The Delannoy number ''D''(3,3) equals 63. The following figure illustrates the 63 Delannoy paths through a 3 × 3 grid: The subset of paths that do not rise above the SW–NE diagonal are counted by a related family of numbers, the Schröder numbers. 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「Delannoy 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.