login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A103936 Theta series of Barnes-Wall lattice in 64 dimensions. 1
1, 0, 0, 0, 9694080, 0, 89754255360, 10164979630080, 639876527832960, 24647440237854720, 646038471835975680, 12399979575839293440, 184026095698230213120, 2200347840694273966080, 21889196776341251850240, 185813171532073386639360, 1373979253438910041038720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

REFERENCES

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

LINKS

Andy Huchala, Table of n, a(n) for n = 0..20000

Index entries for sequences related to Barnes-Wall lattices

EXAMPLE

1 + 9694080*q^8 + 89754255360*q^12 + 10164979630080*q^14 + 639876527832960*q^16 + 24647440237854720*q^18 + 646038471835975680*q^20 + 12399979575839293440*q^22 + 184026095698230213120*q^24 + 2200347840694273966080*q^26 + ...

In terms of H1 = theta_{D4} and H2 = (eta(q) eta(q^2))^8: H1^16 - 384*H1^12*H2 + 38016*H1^8*H2^2 - 743424*H1^4*H2^3 + 9732096*H2^4.

PROG

(Sage)

from sage.modular.etaproducts import qexp_eta; bound = 20;

eta(q) = qexp_eta(ZZ[['q']], bound);

R.<q> = ZZ[];

H1 = ModularForms( Gamma0(2), 2, prec=bound).0;

H1 = R(H1.q_expansion());

H2 = R(q*(eta(q)*eta(q^2))^8);

f = H1^16-384*H1^12*H2+38016*H1^8*H2^2-743424*H1^4*H2^3+9732096*H2^4;

list(f)[:bound] # Andy Huchala, May 01 2021

CROSSREFS

Sequence in context: A250518 A268252 A251504 * A147713 A123322 A258363

Adjacent sequences:  A103933 A103934 A103935 * A103937 A103938 A103939

KEYWORD

nonn,changed

AUTHOR

Eric Rains and N. J. A. Sloane, Sep 27 2005

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 15 08:04 EDT 2021. Contains 343909 sequences. (Running on oeis4.)