A008436 Theta series of {D_9}^{+} packing.

1, 0, 0, 0, 0, 0, 0, 0, 144, 256, 0, 0, 0, 0, 0, 0, 2034, 2304, 0, 0, 0, 0, 0, 0, 7392, 9216, 0, 0, 0, 0, 0, 0, 22608, 23808, 0, 0, 0, 0, 0, 0, 44640, 50688, 0, 0, 0, 0, 0, 0, 93984, 96768, 0, 0, 0, 0, 0, 0, 141120

Offset

0,9

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)^9 + theta_3(q)^9 + theta_4(q)^9)/2 in powers of q^(1/4).

Expansion of (Sum_{k=-oo..oo} q^((k+1/2)^2))^9 + (Sum_{k=-oo..oo} q^(k^2))^9 + (Sum_{k=-oo..oo} (-1)^k * q^(k^2))^9 in powers of q^(1/4). (End)

Example

G.f.: 1 + 144*q^2 + 256*q^(9/4) + 2034*q^4 + 2304*q^(17/4) + ... .

Crossrefs

Cf. A000122 (theta_3(q)), A002448 (theta_4(q)), A008431.

Sequence in context: A159456 A316483 A064563 * A250773 A262245 A134341

Adjacent sequences: A008433 A008434 A008435 * A008437 A008438 A008439

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved