In mathematics, a dodecagonal number is a figurate number that represents a dodecagon. The dodecagonal number for n is given by the formula

The first few dodecagonal numbers are:

A formula for the sum of the reciprocals of the dodecagonal numbers is given by $${\displaystyle \sum _{n=1}^{\infty }{\frac {1}{5n^{2}-4n}}={\frac {5}{16}}\ln \left(5\right)+{\frac {\sqrt {5}}{8}}\ln \left({\frac {1+{\sqrt {5}}}{2}}\right)+{\frac {\pi }{8}}{\sqrt {1+{\frac {2}{\sqrt {5}}}}}.}$$