A004535 Theta series of 14-dimensional unimodular lattice (E7+E7)+.

1, 0, 252, 3136, 17388, 64512, 194656, 501120, 1101996, 2193408, 4195800, 7551936, 12508384, 19934208, 31616064, 48487040, 70404012, 99735552, 142513308, 200515392, 268608312, 353783808, 475911072

Offset

0,3

Links

Table of n, a(n) for n=0..22.

J. H. Conway, A. M. Odlyzko, and N. J. A. Sloane, Extremal Self-Dual Lattices Exist Only in Dimensions 1-8, 12, 14, 15, 23 and 24, Mathematika, 25 (1978), 36-43.

N. Heninger, E. M. Rains, and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006; J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.

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

Formula

G.f.: (theta3^7 + 7*theta3^3*theta2^4)^2 + (theta2^7 + 7*theta2^3*theta3^4)^2.

Example

1 + 252*q^2 + 3136*q^3 + ...

Mathematica

terms = 23; s = (EllipticTheta[3, 0, q]^7 + 7*EllipticTheta[3, 0, q]^3 * EllipticTheta[2, 0, q]^4)^2 + (EllipticTheta[2, 0, q]^7 + 7*EllipticTheta[2, 0, q]^3 * EllipticTheta[3, 0, q]^4)^2 + O[q]^terms // Normal; Join[{1, 0}, Rest[(List @@ s) /. q -> 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 07 2017 *)

Crossrefs

Sequence in context: A104679 A117281 A152466 * A027815 A271496 A218418

Adjacent sequences: A004532 A004533 A004534 * A004536 A004537 A004538

Keyword

nonn

Author

N. J. A. Sloane

Status

approved