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A008893
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Number of equilateral triangles formed by triples of points taken from a hexagonal chunk of side n in the hexagonal lattice.
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3
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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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history;
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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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.]
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FORMULA
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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]
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PROG
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(Maxima) A008893(n):=n*(n+1)*(7*n^2+7*n+2)/4$
makelist(A008893(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
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CROSSREFS
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Cf. A045949, A152041.
Sequence in context: A041114 A015496 A039329 * A168302 A121782 A212784
Adjacent sequences: A008890 A008891 A008892 * A008894 A008895 A008896
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, R. K. Guy
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EXTENSIONS
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Edited May 29 2012 by N. J. A. Sloane, May 29 2012
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STATUS
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approved
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