: Mathematics: centered octagonal number

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centered octagonal number

A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers. The centered octagonal numbers are the same as the odd square numbers. Thus, the nth odd square number and tth centered octagonal number is given by the formula
${\\displaystyle O_{n}=(2n-1)^{2}=4n^{2}-4n+1|(2t+1)^{2}=4t^{2}+4t+1.}$

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