Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)


gives the n^(th) triangular number .

gives the n^(th) r-gonal number TemplateBox[{P, n, { , r}}, Subsuperscript].


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • PolygonalNumber[n] is generically defined as TemplateBox[{{n, +, 1}, 2}, Binomial].
  • PolygonalNumber[r,n] is generically defined as .
  • PolygonalNumber[r,n] can be interpreted as the number of points arranged in the form of n-1 polygons of r sides. For instance for r=3 and n=4:
  • PolygonalNumber automatically threads over lists.
Introduced in 2016