A centered octagonal number is a centered figurate number that represents an octagon with a dot in the center and all other dots surrounding the center dot in successive octagonal layers. The centered octagonal numbers are the same as the odd square numbers. Thus, the nth odd square number and tth centered octagonal number is given by the formula
The first few centered octagonal numbers are
- Teo, Boon K.; Sloane, N. J. A. (1985), "Magic numbers in polygonal and polyhedral clusters" (PDF), Inorganic Chemistry, 24 (26): 4545–4558, doi:10.1021/ic00220a025.
- Sloane, N. J. A. (ed.). "Sequence A016754 (Odd squares: (2n-1)^2. Also centered octagonal numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.