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# Centered nonagonal number

A centered nonagonal 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 is given by the formula

${(3n-1)(3n-2)}\over2$.

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 is also a centered nonagonal number.

Thus, the first few centered nonagonal numbers are

1, 10, 28, 55, 91, 136, 190, 253, 325, 406, 496, 595, 703, 820, 946