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In mathematics, a Motzkin number for a given number ''n'' is the number of different ways of drawing non-intersecting chords between ''n'' points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin, and have very diverse applications in geometry, combinatorics and number theory. Motzkin numbers for form the sequence: : 1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 25669818476, 73007772802, 208023278209, 593742784829, ... == Examples == The following figure shows the 9 ways to draw non-intersecting chords between 4 points on a circle. The following figure shows the 21 ways to draw non-intersecting chords between 5 points on a circle. 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「Motzkin number」の詳細全文を読む スポンサード リンク
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