A008659 Theta series of direct sum of 3 copies of D_4 lattice.

1, 72, 1800, 17568, 57096, 225072, 439200, 1210176, 1826568, 4269096, 5626800, 11595744, 13931424, 26733168, 30254400, 54917568, 58449672, 102229776, 106727400, 178279200, 178482096, 295282944, 289893600, 463416768, 445682592

Offset

0,2

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 119.

Srinivasa Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988, pp. 116, equation (4).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Index entries for sequences related to D_4 lattice

Formula

Expansion of (8 * E_6(x^2) - E_6(x)) / 7 in powers of x where E_6() is an Eisenstein series.

Mathematica

terms = 25; E6[q_] = 1 - 504 Sum[k^5 q^(2 k)/(1 - q^(2 k)), {k, 1, terms}]; s = (8*E6[q^2] - E6[q])/7 + O[q]^(2 terms); CoefficientList[s, q^2][[1 ;; terms]] (* Jean-François Alcover, Jul 04 2017 *)

Prog

(PARI) {a(n) = if( n<1, n==0, 72 * (sigma( n, 5) - if( n%2, 0, 8 * sigma( n/2, 5))))} /* Michael Somos, Jul 16 2004 */

Crossrefs

Sequence in context: A234209 A280807 A268749 * A263974 A344029 A187303

Adjacent sequences: A008656 A008657 A008658 * A008660 A008661 A008662

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved