A008662 Theta series of direct sum of 6 copies of D_4 lattice.

1, 144, 8784, 294336, 5883984, 71916768, 547468992, 2882049408, 12927121488, 45761350608, 150532923744, 416276152128, 1118182645440, 2614241349216, 6094718050176, 12618123283584, 26478496036944

Offset

0,2

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 119.

Links

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

Index entries for sequences related to D_4 lattice

Example

G.f. = 1 + 144*q + 8784*q^2 + 294336*q^3 + 5883984*q^4 + 71916768*q^5 + ... - Michael Somos, May 27 2022

Mathematica

terms = 17; s = (1/2 (EllipticTheta[3, 0, q]^4 + EllipticTheta[4, 0, q]^4) )^6 + O[q]^(2 terms); CoefficientList[s, q^2] (* Jean-François Alcover, Jul 08 2017 *)
a[ n_] := With[{e1 = q*QPochhammer[q]^24, e2 = q^2*QPochhammer[q^2]^24}, SeriesCoefficient[(e1 + 64* e2)^3 / (e1* e2), {q, 0, n}]]; (* Michael Somos, May 27 2022 *)

Crossrefs

Sequence in context: A182920 A299858 A308285 * A181014 A035821 A231854

Adjacent sequences: A008659 A008660 A008661 * A008663 A008664 A008665

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved