A008446 Theta series of A_6 lattice.

1, 42, 210, 350, 882, 1050, 1750, 2100, 3570, 3066, 5250, 5124, 7350, 7350, 10500, 8064, 14322, 12600, 15330, 15750, 22050, 16814, 25620, 22260, 29750, 25242, 36750, 28700, 44100, 35364, 40320, 42000, 57330, 42700, 63000, 50442, 64386, 57540, 78750, 56448

Offset

0,2

References

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

Links

Table of n, a(n) for n=0..39.

G. Nebe and N. J. A. Sloane, Home page for this lattice

Example

1 + 42*q^2 + 210*q^4 + 350*q^6 + 882*q^8 + 1050*q^10 + 1750*q^12 + 2100*q^14 + 3570*q^16 + 3066*q^18 + 5250*q^20 + 5124*q^22 + 7350*q^24 + 7350*q^26 + 10500*q^28 + 8064*q^30 + 14322*q^32 + 12600*q^34 + 15330*q^36 + 15750*q^38 + 22050*q^40 + 16814*q^42 + 25620*q^44 + ...

Mathematica

terms = 40; f[q_] = LatticeData["A6", "ThetaSeriesFunction"][-I Log[q]/Pi]; s = Series[f[q], {q, 0, 2 terms}]; DeleteCases[CoefficientList[s, q^(1/2) ] // Round, 0][[1 ;; terms]] (* Jean-François Alcover, Jul 04 2017 *)

Prog

(Magma) L:=Lattice("A", 6); T1<q> := ThetaSeries(L, 120);

Crossrefs

Sequence in context: A299817 A236278 A236271 * A255424 A122232 A193392

Adjacent sequences: A008443 A008444 A008445 * A008447 A008448 A008449

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Status

approved