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Centered octagonal number
Centered figurate number that represents an octagon with a dot in the center From Wikipedia, the free encyclopedia
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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.[1] The centered octagonal numbers are the same as the odd square numbers.[2] Thus, the nth odd square number and tth centered octagonal number is given by the formula


The first few centered octagonal numbers are[2]
Calculating Ramanujan's tau function on a centered octagonal number yields an odd number, whereas for any other number the function yields an even number.[2]
is the number of 2x2 matrices with elements from 0 to n that their determinant is twice their permanent.
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