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The lazy caterer's sequence, more formally known as the central polygonal numbers, describes the maximum number of pieces of a circle (a pancake or pizza is usually used to describe the situation) that can be made with a given number of straight cuts. For example, three cuts across a pancake will produce six pieces if the cuts all meet at a common point, but seven if they do not. This problem can be formalized mathematically as one of counting the cells in an arrangement of lines; for generalizations to higher dimensions, ''see'' arrangement of hyperplanes. The analogue of this sequence in 3 dimensions is the cake number. ==Formula and sequence== The maximum number ''p'' of pieces that can be created with a given number of cuts ''n'', where ''n'' ≥ 0, is given by the formula : Using binomial coefficients, the formula can be expressed as : This sequence , starting with , results in :1, 2, 4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172, 191, 211, ... Each number equals 1 plus a triangular number. 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「lazy caterer's sequence」の詳細全文を読む スポンサード リンク
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