A015235 - OEIS

A015235

Theta series of lattice Kappa_8.

1, 0, 132, 192, 828, 1152, 2796, 2880, 6828, 5376, 14904, 10944, 20772, 18432, 40224, 25920, 53964, 41472, 76452, 58176, 107784, 69504, 156816, 101376, 163284, 131328, 259032, 147072, 295200, 206208, 357480, 250560, 432780, 269568, 576072, 365184, 555804, 426240

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

OFFSET

0,3

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 161.

LINKS

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

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

EXAMPLE

G.f. = 1 + 132*q^4 + 192*q^6 + ...

PROG

(Sage)

L = [1, 0, 132, 192, 828, 1152, 2796, 2880, 6828, 5376]

M = ModularForms(Gamma0(12), 4)

bases = [_.q_expansion(35) for _ in M.integral_basis()]

f = sum(x*y for (x, y) in zip(bases, L)); list(f) # Andy Huchala, Jul 23 2021

CROSSREFS

Cf. A015236 (K_7), A015233 (K_9), A015232 (K_10), A015229 (K_11), A004010 (K_12), A029897 (K_13), A047628 (K_14).

Sequence in context: A354812 A030026 A102474 * A204649 A224548 A253510

Adjacent sequences: A015232 A015233 A015234 * A015236 A015237 A015238

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Sean A. Irvine, Feb 26 2020

STATUS

approved