Dodecagonal number

• The dodecagonal number for n can be calculated by adding the square of n to four times the (n - 1)th pronic number, or to put it algebraically, $D\_n\; =\; n^2\; +\; 4(n^2\; -\; n)$.

• Dodecagonal numbers consistently alternate parity, and in base 10, their units place digits follow the pattern 1, 2, 3, 4, 5, 6, 7, 8, 9, 0.

• By the Fermat polygonal number theorem, every number is the sum of at most 12 dodecagonal numbers.

• $D\_n$ is the sum of the first n natural numbers congruent to 1 mod 10.

• $D\_\{n+1\}$ is the sum of all odd numbers from 4n+1 to 6n+1.

A formula for the sum of the reciprocals of the dodecagonal numbers is given by

\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}}}.

• Polygonal number
• Figurate number
• Dodecagon

{{Figurate numbers}}

{{Classes of natural numbers}}

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Category:Figurate numbers