

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
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OFFSET

0,2


COMMENTS

The hexagonal lattice is the familiar 2dimensional 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



FORMULA

a(n) = n*(n+1)*(7*n^2+7*n+2)/4.
G.f.: 2*x*(4*x^2+13*x+4)/(x1)^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$


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



