A008662 - OEIS

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

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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