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 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 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.] 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

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