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A008657
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Theta series of direct sum of 6 copies of hexagonal lattice.
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2
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1, 36, 540, 4356, 20556, 60696, 137916, 325152, 658476, 1023012, 1999080, 3112560, 4446828, 7207992, 10755936, 13150296, 20963052, 27538056, 33706908, 47989008, 64050696, 70696224, 103079952, 124752096, 142308684, 189312156, 237450312, 248276484, 344385504, 397677816
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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.
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 110.
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LINKS
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MATHEMATICA
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terms = 23; s = ((EllipticTheta[3, 0, q]^3 + EllipticTheta[3, Pi/3, q]^3 + EllipticTheta[3, 2 Pi/3, q]^3)/(3*EllipticTheta[3, 0, q^3]))^6 + O[q]^(2 terms); CoefficientList[s, q^2] (* Jean-François Alcover, Jul 08 2017, from LatticeData(A2) *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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