A004017 Theta series of E_8 lattice with respect to deep hole.

16, 128, 448, 1024, 2016, 3584, 5504, 8192, 12112, 16128, 21312, 28672, 35168, 44032, 56448, 65536, 78624, 96896, 109760, 129024, 154112, 170496, 194688, 229376, 252016, 281344, 327040, 352256, 390240, 451584, 476672, 524288, 596736, 628992

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 122.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Fern Gossow, Lyndon-like cyclic sieving and Gauss congruence, arXiv:2410.05678 [math.CO], 2024. See p. 26.
• G. Nebe and N. J. A. Sloane, Home page for this lattice

Crossrefs

Equals 16 * A007331(n).

Programs

Mathematica

QP = QPochhammer; s = QP[-1, q]^16 QP[q]^8 / 2^12 + O[q]^34; CoefficientList[s, q] (* Jean-François Alcover, Jul 04 2017 *)

Extensions

a(8) corrected and more terms from Sean A. Irvine, Oct 18 2015