Hexagonal Number
A Figurate Number and 6-Polygonal Number of the form 
. The first few are 1, 6, 15, 28, 45, ... (Sloane's A000384). The Generating Function of the hexagonal numbers
Every hexagonal number is a Triangular Number since
In 1830, Legendre
(1979) proved that every number larger than 1791 is a sum of four hexagonal numbers, and Duke andSchulze-Pillot (1990) improved this to three hexagonal numbers for every sufficiently large integer. The numbers 11and 26 can only be represented as a sum using the maximum possible of six hexagonal numbers: |  |  | |
 | |  |
See also Figurate Number, Hex Number, Triangular Number
References
Duke, W. and Schulze-Pillot, R. ``Representations of Integers by Positive Ternary Quadratic Forms and Equidistribution of Lattice Points on Ellipsoids.'' Invent. Math. 99, 49-57, 1990. Guy, R. K. ``Sums of Squares.'' §C20 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 136-138, 1994. Legendre, A.-M. Théorie des nombres, 4th ed., 2 vols. Paris: A. Blanchard, 1979. Sloane, N. J. A. SequenceA000384/M4108in ``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.
- Uniplanar Double Point
- Unipotent
- Unique
- Unique Factorization Theorem
- Unit
- Unital
- Unitary Aliquot Sequence
- Unitary Amicable Pair
- Unitary Divisor
- Unitary Group
- Unitary Matrix
- Unitary Multiperfect Number
- Unitary Multiplicative Character
- Unitary Perfect Number
- Unitary Sociable Numbers
- Unitary Transformation
- Unitary Unimodular Group
- Unit Circle
- Unit Disk
- Unit Fraction
- Unit Matrix
- Unit Point
- Unit Ring
- Unit Sphere
- Unit Square