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 (terms 0..1000 from G. C. Greubel)
J. McKay and A. Sebbar, Fuchsian groups, automorphic functions and Schwarzians, Math. Ann., 318 (2000), 255-275.
G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2
FORMULA
Expansion of (theta_3(z)*theta_3(3z) + theta_2(z)*theta_2(3z))^4.
MAPLE
A008655 := proc(n)
add( A004016(i)*x^i, i=0..n) ;
coeftayl(%^4, x=0, n) ;
end proc: # R. J. Mathar, Feb 22 2021
MATHEMATICA
terms = 28; s = (EllipticTheta[3, 0, q]^3 + EllipticTheta[3, Pi/3, q]^3 + EllipticTheta[3, 2 Pi/3, q]^3)^4/(81*EllipticTheta[3, 0, q^3]^4) + O[q]^(2 terms); CoefficientList[s, q^2][[1 ;; terms]] (* Jean-François Alcover, Jul 07 2017, from LatticeData(A2) *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved