: Mathematics: centered nonagonal number

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centered nonagonal number

A centered nonagonal number (or centered enneagonal number) is a centered figurate number that represents a nonagon with a dot in the center and all other dots surrounding the center dot in successive nonagonal layers. The centered nonagonal number for n layers is given by the formula
${\\displaystyle Nc(n)={\ rac {(3n-2)(3n-1)}{2}}.}$
Multiplying the (n - 1)th triangular number by 9 and then adding 1 yields the nth centered nonagonal number, but centered nonagonal numbers have an even simpler relation to triangular numbers: every third triangular number (the 1st, 4th, 7th, etc.) is also a centered nonagonal number.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Centered_nonagonal_number)

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