A004017 - OEIS

A004017

Theta series of E_8 lattice with respect to deep hole.
(Formerly M5009)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

Table of n, a(n) for n=1..34.

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

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 *)

CROSSREFS

Equals 16 * A007331(n).

Sequence in context: A253319 A367070 A291460 * A167471 A153115 A138331

Adjacent sequences: A004014 A004015 A004016 * A004018 A004019 A004020

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

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

STATUS

approved