Editing Centered triangular number (section)

{{Short description|Centered figurate number that represents a triangle with a dot in the center}}
{{Use American English|date=March 2021}}
{{Use mdy dates|date=March 2021}}
{{no footnotes|date=June 2014}}

A '''centered''' (or '''centred''') '''triangular number''' is a [[Centered number|centered]] [[figurate number]] that represents an [[equilateral triangle]] with a dot in the center and all its other dots surrounding the center in successive equilateral triangular layers.

This is also the number of points of a hexagonal lattice with nearest-neighbor coupling whose distance from a given point
is less than or equal to <math>n</math>.

The following image shows the building of the centered triangular numbers by using the associated figures: at each step, the previous triangle (shown in red) is surrounded by a triangular layer of new dots (in blue).

[[File:Centered triangular numbers.svg|946x946px|construction]]
[[File:centered_triangular_numbers_hex_grid.svg|thumb|The first eight centered triangular numbers on a [[hex grid]] ]]