A045819 Theta series of E_8 lattice with respect to midpoint of edge.

2, 56, 252, 688, 1514, 2664, 4396, 7056, 9828, 13720, 19264, 24336, 31502, 40880, 48780, 59584, 74592, 86688, 101308, 123088, 137844, 159016, 190764, 207648, 235986, 275184, 297756, 335664, 384160, 410760, 453964, 520816, 553896, 601528

Offset

0,1

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, 1999, p. 123.

Links

Table of n, a(n) for n=0..33.

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

Formula

G.f.: (1/2)*(theta_2^2*theta_3^6 + theta_2^6*theta_3^2).

a(n) = 2*sigma_3(2n+1). - Benoit Cloitre, Apr 12 2003

a(n) = 2 * A045823(n). - Alois P. Heinz, Mar 21 2021

Sum_{k=0..n} a(k) ~ (15*zeta(4)/4) * n^4. - Amiram Eldar, Dec 12 2023

Example

2*q^(1/2) + 56*q^(3/2) + 252*q^(5/2) + ...

Mathematica

a[n_] := 2 DivisorSigma[3, 2 n + 1]; Table[a[n], {n, 0, 33}] (* Jean-François Alcover, Jul 06 2017, after Benoit Cloitre *)

Crossrefs

Cf. A001158, A008438, A013662, A045823.

Sequence in context: A376667 A037176 A376851 * A281198 A287988 A193830

Adjacent sequences: A045816 A045817 A045818 * A045820 A045821 A045822

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Benoit Cloitre, Apr 12 2003

Status

approved