A008435 Theta series of {D_7}^{+} packing.

1, 0, 0, 0, 0, 0, 0, 64, 84, 0, 0, 0, 0, 0, 0, 448, 574, 0, 0, 0, 0, 0, 0, 1344, 1288, 0, 0, 0, 0, 0, 0, 2688, 3444, 0, 0, 0, 0, 0, 0, 4928, 4424, 0, 0, 0, 0, 0, 0, 8064, 9240, 0, 0, 0, 0, 0, 0, 11200, 11088, 0, 0, 0

Offset

0,8

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 120.

Links

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

Eric Weisstein's World of Mathematics, Jacobi Theta Functions

Formula

From Seiichi Manyama, Oct 21 2018: (Start)

Expansion of (theta_2(q)^7 + theta_3(q)^7 + theta_4(q)^7)/2 in powers of q^(1/4).

Expansion of (Sum_{k=-inf..inf} q^((k+1/2)^2))^7 + (Sum_{k=-inf..inf} q^(k^2))^7 + (Sum_{k=-inf..inf} (-1)^k * q^(k^2))^7 in powers of q^(1/4). (End)

Example

G.f.: 1 + 64*q^(7/4) + 84*q^2 + 448*q^(15/4) + 574*q^4 + ... .

Crossrefs

Cf. A008429.

Sequence in context: A057372 A057442 A141817 * A223083 A302169 A302640

Adjacent sequences: A008432 A008433 A008434 * A008436 A008437 A008438

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved