Sequence of Square Centered Hexagonal Numbers/Mistake

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Source Work

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary
$169$


Mistake

The smallest square hexagonal number, apart from $1$ [is $169$]. The next smallest are $32, 761$ and $6,355,441$.


The hexagonal numbers are those of this form:

HexagonNumbers.png


The sequence of hexagonal numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, \ldots$


What is intended here is:

The smallest square centered hexagonal number, apart from $1$.

The centered hexagonal numbers are those of this form:

CenteredHexagonNumbers.png


The sequence of centered hexagonal numbers, for $n \in \Z_{> 0}$, begins:

$1, 7, 19, 37, 61, 91, 127, 169, 217, 271, 331, 397, 469, 547, 631, 721, 817, 919, \ldots$

$\blacksquare$


Sources