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A hexagonal number is a figurate number. The ''n''th hexagonal number ''h''n is the number of ''distinct'' dots in a pattern of dots consisting of the ''outlines'' of regular hexagons with sides up to n dots, when the hexagons are overlaid so that they share one vertex. The formula for the ''n''th hexagonal number : :where ''M''''p'' is a Mersenne prime. No odd perfect numbers are known, hence all known perfect numbers are hexagonal. :For example, the 2nd hexagonal number is 2×3 = 6; the 4th is 4×7 = 28; the 16th is 16×31 = 496; and the 64th is 64×127 = 8128. The largest number that cannot be written as a sum of at most four hexagonal numbers is 130. Adrien-Marie Legendre proved in 1830 that any integer greater than 1791 can be expressed in this way. Hexagonal numbers can be rearranged into rectangular numbers of size ''n'' by (2''n''−1). Hexagonal numbers should not be confused with centered hexagonal numbers, which model the standard packaging of Vienna sausages. To avoid ambiguity, hexagonal numbers are sometimes called "cornered hexagonal numbers". ==Test for hexagonal numbers== One can efficiently test whether a positive integer ''x'' is an hexagonal number by computing : If ''n'' is an integer, then ''x'' is the ''n''th hexagonal number. If ''n'' is not an integer, then ''x'' is not hexagonal. 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「hexagonal number」の詳細全文を読む スポンサード リンク
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