A008433 Theta series of {D_5}^{+} packing.

1, 0, 0, 0, 0, 16, 0, 0, 40, 0, 0, 0, 0, 80, 0, 0, 90, 0, 0, 0, 0, 160, 0, 0, 240, 0, 0, 0, 0, 240, 0, 0, 200, 0, 0, 0, 0, 400, 0, 0, 560, 0, 0, 0, 0, 496, 0, 0, 400, 0, 0, 0, 0, 560, 0, 0, 800, 0, 0, 0, 0, 880, 0, 0, 730

Offset

0,6

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)^5 + theta_3(q)^5 + theta_4(q)^5)/2 in powers of q^(1/4).

Expansion of (Sum_{k=-oo..oo} q^((k+1/2)^2))^5 + (Sum_{k=-oo..oo} q^(k^2))^5 + (Sum_{k=-oo..oo} (-1)^k * q^(k^2))^5 in powers of q^(1/4). (End)

Example

G.f.: 1 + 16*q^(5/4) + 40*q^2 + 80*q^(13/4) + 90*q^4 + ... .

Crossrefs

Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A005930.

Sequence in context: A169767 A225611 A173293 * A347803 A010111 A118067

Adjacent sequences: A008430 A008431 A008432 * A008434 A008435 A008436

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved