Pentagonal Number
A Polygonal Number of the form 
. The first few are 1, 5, 12, 22, 35, 51, 70, ... (Sloane's A000326).The Generating Function for the pentagonal numbers is
Every pentagonal number is 1/3 of a Triangular Number.
The so-called generalized pentagonal numbers are given by with 
, 
, 
, ..., the firstfew of which are 0, 1, 2, 5, 7, 12, 15, 22, 26, 35, ... (Sloane's A001318).
References
Guy, R. K. ``Sums of Squares.'' §C20 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 136-138, 1994. Pappas, T. ``Triangular, Square & Pentagonal Numbers.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, p. 214, 1989. Sloane, N. J. A. SequencesA000326/M3818and A001318/M1336in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.
- Appell Hypergeometric Function
- Appell Polynomial
- Appell Transformation
- Apple
- Approximately Equal
- Approximation Theory
- Apéry's Constant
- Arakelov Theory
- Arbelos
- Arborescence
- Arboricity
- Arc
- Arch
- Archimedean Solid
- Archimedean Solid Stellation
- Archimedean Spiral
- Archimedean Spiral Inverse Curve
- Archimedean Valuation
- Archimedes Algorithm
- Archimedes' Axiom
- Archimedes' Cattle Problem
- Archimedes' Circles
- Archimedes' Constant
- Archimedes' Hat-Box Theorem
- Archimedes' Lemma