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The centered polygonal numbers are a class of series of figurate numbers, each formed by a central dot, surrounded by polygonal layers with a constant number of sides. Each side of a polygonal layer contains one dot more than a side in the previous layer, so starting from the second polygonal layer each layer of a centered ''k''-gonal number contains ''k'' more points than the previous layer. ==Examples== Each sequence is a multiple of the triangular numbers plus 1. For example, the centered square numbers are four times the triangular numbers plus 1. These series consist of the *centered triangular numbers 1,4,10,19,31,... *centered square numbers 1,5,13,25,41,... () *centered pentagonal numbers 1,6,16,31,51,... () *centered hexagonal numbers 1,7,19,37,61,... () *centered heptagonal numbers 1,8,22,43,71,... () *centered octagonal numbers 1,9,25,49,81,... () *centered nonagonal numbers 1,10,28,55,91,... (, which include all even perfect numbers except 6) *centered decagonal numbers 1,11,31,61,101,... () and so on. The following diagrams show a few examples of centered polygonal numbers and their geometric construction. Compare these diagrams with the diagrams in Polygonal 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「Centered polygonal number」の詳細全文を読む スポンサード リンク
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