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. 111.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..10000
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
FORMULA
Nonzero coefficients in expansion of theta_3(q)*theta_3(q^3) + theta_2(q)*theta_2(q^3).
The corresponding powers of q are A003136. - Robert Israel, Jul 29 2016
MAPLE
S:=series(JacobiTheta2(0, q)*JacobiTheta2(0, q^3)+JacobiTheta3(0, q)*JacobiTheta3(0, q^3), q, 1001):
subs(0=NULL, [seq(coeff(S, q, j), j=0..1000)]); # Robert Israel, Jul 29 2016
MATHEMATICA
s = EllipticTheta[2, 0, q]*EllipticTheta[2, 0, q^3] + EllipticTheta[3, 0, q]* EllipticTheta[3, 0, q^3] + O[q]^1000; CoefficientList[s, q] /. 0 -> Nothing (* Jean-François Alcover, Sep 19 2016, after Robert Israel *)
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved