A055379 16*a(n) gives theta series of the shadow of the 24-dimensional odd Leech lattice.

3, 12216, 1049332, 24866496, 289421466, 2150562080, 11720932296, 50917793280, 186017041471, 592764490128, 1691223619836, 4404312868096, 10623285300642, 24004367672640, 51272935258008, 104280162643968, 203151521341206

Offset

1,1

References

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

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

E. M. Rains and N. J. A. Sloane, The Shadow Theory of Modular and Unimodular Lattices, J. Number Theory, 73 (1998), 359-389.

Formula

G.f.: (1/16)*( theta2(z)^24 + 3*theta4(2*z)^8 * theta2(z)^16 + (3/16)*theta4(2*z)^16 * theta2(z)^8 ).

Mathematica

CoefficientList[Series[(EllipticTheta[2, 0, q^(1/2)]^24 + 3*EllipticTheta[2, 0, q^(1/2)]^16*EllipticTheta[4, 0, q]^8 + (3/16)*EllipticTheta[2, 0, q^(1/2)]^8*EllipticTheta[4, 0, q]^16)/16, {q, 0, 30}], q] (* G. C. Greubel, Mar 15 2022 *)

Crossrefs

Cf. A027859.

Sequence in context: A280655 A262651 A309246 * A047777 A195834 A124393

Adjacent sequences: A055376 A055377 A055378 * A055380 A055381 A055382

Keyword

nonn

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jun 22 2000

Status

approved