Centered nonagonal number

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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

.

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

See also regular nonagonal number.