A023922 Theta series of A*_10 lattice.

1, 0, 0, 0, 0, 22, 0, 0, 0, 110, 0, 110, 330, 0, 660, 924, 990, 0, 0, 0, 2662, 0, 1980, 4840, 0, 6534, 7260, 9460, 0, 0, 0, 15840, 0, 10230, 21780, 0, 27830, 32670, 33660, 0, 0, 0, 50820, 0, 30140, 71236, 0, 84700, 87120, 99000, 0, 0, 0, 136840, 0

Offset

0,6

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 114.

Links

Table of n, a(n) for n=0..54.

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

K. Ono, On the Circular Summation of the Eleventh Powers of Ramanujan's Theta Function, Journal of Number Theory, Volume 76, Issue 1, May 1999, Pages 62-65.

Formula

G.f.: eta^11(q)/eta(q^11) + 800*q^5*eta^11(q^11)/eta(11) - 9*P11(q)*eta^11(q) + (308/3)*A(q) + (22/3)*B(q), where P11(q) is the g.f. for A213256, A(q) is the g.f. for A065103, B(q) is the g.f. for A065099, and eta is the Dedekind eta function [from Ono]. - Sean A. Irvine, Jun 16 2019

Example

G.f. = 1 + 22*q^5 + 110*q^9 + 110*q^11 + 330*q^12 + ... - Sean A. Irvine, Jun 16 2019

Crossrefs

Sequence in context: A062012 A104786 A104787 * A022064 A225343 A252670

Adjacent sequences: A023919 A023920 A023921 * A023923 A023924 A023925

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

More terms from Sean A. Irvine, Jun 16 2019

Status

approved