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Theta series of direct sum of 5 copies of hexagonal lattice.
1

%I #16 Oct 19 2018 09:13:53

%S 1,30,360,2190,7230,14976,32760,72060,92520,177150,280800,351360,

%T 527790,856860,864720,1362816,1850430,2004480,2657160,3909660,3609216,

%U 5260380,6588000,6716160,8419320

%N Theta series of direct sum of 5 copies of hexagonal lattice.

%C The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice.

%D J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 110.

%H Seiichi Manyama, <a href="/A008656/b008656.txt">Table of n, a(n) for n = 0..10000</a>

%H G. Nebe and N. J. A. Sloane, <a href="http://www.math.rwth-aachen.de/~Gabriele.Nebe/LATTICES/A2.html">Home page for hexagonal (or triangular) lattice A2</a>

%t terms = 25; 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]))^5 + O[q]^(2 terms); CoefficientList[s, q^2] (* _Jean-François Alcover_, Jul 08 2017, from LatticeData(A2) *)

%Y Cf. A004016.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_