Nonagonal number

A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided polygon).^[1] However, unlike the triangular and square numbers, the patterns involved in the construction of nonagonal numbers are not rotationally symmetrical. Specifically, the nth nonagonal number counts the dots in a pattern of n nested nonagons, all sharing a common corner, where the ith nonagon in the pattern has sides made of i dots spaced one unit apart from each other. The nonagonal number for n is given by the formula:^[2]

${\displaystyle {\frac {n(7n-5)}{2}}}$.