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A045819 Theta series of E_8 lattice with respect to midpoint of edge. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

REFERENCES

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

LINKS

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

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

FORMULA

(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

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-Fran├žois Alcover, Jul 06 2017, after Benoit Cloitre *)

CROSSREFS

Cf. A001158, A008438.

Sequence in context: A210932 A278842 A037176 * 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

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Last modified January 19 19:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)