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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Examples

			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 + ...
		

References

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

Links

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

Programs

Magma

L:=Lattice("A",6); T1 := ThetaSeries(L,120);

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 *)