Definition:Centered Hexagonal Number
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Definition
A centered hexagonal number is a figurate number which is represented by:
- a point in the center
- all other points surrounding the center at the points of a triangular lattice.
Examples of Centered Hexagonal Numbers
The first few centered hexagonal numbers are as follows:
Sequence of Centered Hexagonal Numbers
The sequence of centered hexagonal numbers, for $n \in \Z_{> 0}$, begins:
- $1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, \ldots$
Also known as
A centered hexagonal number can also be referred to as a hex number.
However, as this can be confused with a hexagonal number this neat and compact term is discouraged on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Also see
- Results about centered hexagonal numbers can be found here.
Linguistic Note
A centered hexagonal number is rendered in British English as centred hexagonal number, on account of the British spelling of centre.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $19$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $37$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $19$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $37$