A008657 Theta series of direct sum of 6 copies of hexagonal lattice.

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

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.

References

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

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2

Mathematica

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) *)

Crossrefs

Cf. A004016.

Sequence in context: A268635 A233101 A183616 * A134289 A329913 A200708

Adjacent sequences: A008654 A008655 A008656 * A008658 A008659 A008660

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Seiichi Manyama, Oct 19 2018

Status

approved