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A008433 Theta series of {D_5}^{+} packing. 1
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 (list; graph; refs; listen; history; text; internal format)
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=-inf..inf} q^((k+1/2)^2))^5 + (Sum_{k=-inf..inf} q^(k^2))^5 + (Sum_{k=-inf..inf} (-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 * A010111 A118067 A037217

Adjacent sequences:  A008430 A008431 A008432 * A008434 A008435 A008436

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 16 13:43 EST 2019. Contains 319193 sequences. (Running on oeis4.)