Centered figurate number that represents an octagon with a dot in the center
A centered octagonal number is a centeredfigurate 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 oddsquare numbers.[2] Thus, the nth odd square number and tth centered octagonal number is given by the formula
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.