A '''centered nonagonal number''' is a [[centered number|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
:<math>{(3n-1)(3n-2)}\over2</math>.
Multiplying the (''n'' - 1)th [[triangular number]] by 9 and then adding 1 yields the ''n''th 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 (number)|1]], [[10 (number)|10]], [[28 (number)|28]], [[55 (number)|55]], [[91 (number)|91]], 136, [[190 (number)|190]], 253, 325, 406, [[496 (number)|496]], 595, 703, 820, 946
See also regular [[nonagonal number]].
[[Category:Number sequences]]
[[fr:Nombre ennéagonal centré]]
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