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An octagonal number is a figurate number that represents an octagon. The octagonal number for ''n'' is given by the formula 3''n''2 - 2''n'', with ''n'' > 0. The first few octagonal numbers are: 1, 8, 21, 40, 65, 96, 133, 176, 225, 280, 341, 408, 481, 560, 645, 736, 833, 936 Octagonal numbers can be formed by placing triangular numbers on the four sides of a square. To put it algebraically, the ''n''-th octagonal number is : The octagonal number for ''n'' can also be calculated by adding the square of ''n'' to twice the (''n - 1'')th pronic number. Octagonal numbers consistently alternate parity. Octagonal numbers are occasionally referred to as "star numbers," though that term is more commonly used to refer to centered dodecagonal numbers.〔.〕 ==Test for octagonal numbers== Solving the formula for the ''n''-th octagonal number, for ''n'' gives : An arbitrary number ''x'' can be checked for octagonality by putting it in this equation. If ''n'' is an integer, then ''x'' is the ''n''-th octagonal number. If ''n'' is not an integer, then ''x'' is not octagonal. 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「octagonal number」の詳細全文を読む スポンサード リンク
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