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.
- Characteristic Function
- Squareful
- Square Gyrobicupola
- Square Integrable
- Square Knot
- Square Matrix
- Square Number
- Square Orthobicupola
- Square Packing
- Square Polyomino
- Square Pyramid
- Square Pyramidal Number
- Square Quadrants
- Square Root
- Square Root Inequality
- Square Root Method
- Square Triangular Number
- Square Wave
- Squaring
- Squeezing Theorem
- s-Run
- S-Signature
- SSS Theorem
- Stability
- Stability Matrix