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In mathematics, the cake number, denoted by ''Cn'', is the maximum number of regions into which a 3-dimensional cube can be partitioned by exactly ''n'' planes. The cake number is so-called because one may imagine each partition of the cube by a plane as a slice made by a knife through a cube-shaped cake. The values of ''Cn'' for increasing are given by The cake numbers are the 3-dimensional analogue of the 2-dimensional lazy caterer's sequence; the difference between successive cake numbers also gives the lazy caterer's sequence. == General formula == If ''n''! denotes the factorial, and we denote the binomial coefficients by : and we assume that ''n'' planes are available to partition the cube, then the number is: : 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「cake number」の詳細全文を読む スポンサード リンク
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