login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A008893 Number of equilateral triangles formed by triples of points taken from a hexagonal chunk of side n in the hexagonal lattice. 6
0, 8, 66, 258, 710, 1590, 3108, 5516, 9108, 14220, 21230, 30558, 42666, 58058, 77280, 100920, 129608, 164016, 204858, 252890, 308910, 373758, 448316, 533508, 630300, 739700, 862758, 1000566, 1154258, 1325010, 1514040, 1722608, 1952016, 2203608, 2478770 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice. Here we consider a hexagonal chunk of the lattice in which each bounding edge contains n+1 points.
LINKS
N. J. A. Sloane, Illustration for a(1)=8. [The drawing was made for a different offset, so it says a(2)=8.]
FORMULA
a(n) = n*(n+1)*(7*n^2+7*n+2)/4.
G.f.: -2*x*(4*x^2+13*x+4)/(x-1)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009]
PROG
(Maxima) A008893(n):=n*(n+1)*(7*n^2+7*n+2)/4$
makelist(A008893(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
CROSSREFS
Sequence in context: A226126 A039329 A230736 * A168302 A121782 A212784
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited May 29 2012 by N. J. A. Sloane, May 29 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 29 16:58 EST 2024. Contains 370426 sequences. (Running on oeis4.)