A008893 Number of equilateral triangles formed by triples of points taken from a hexagonal chunk of side n in the hexagonal lattice.

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

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

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

N. J. A. Sloane, Illustration for a(1)=8. [The drawing was made for a different offset, so it says a(2)=8.]

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

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

Cf. A045949, A152041.

Sequence in context: A226126 A039329 A230736 * A168302 A121782 A212784

Adjacent sequences: A008890 A008891 A008892 * A008894 A008895 A008896

Keyword

nonn,easy

Author

N. J. A. Sloane, R. K. Guy

Extensions

Edited May 29 2012 by N. J. A. Sloane, May 29 2012

Status

approved