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A008429 Theta series of D_7 lattice. 3
1, 84, 574, 1288, 3444, 4424, 9240, 11088, 18494, 19740, 34440, 31304, 52808, 52248, 74048, 71120, 110964, 94864, 145222, 132888, 181384, 163856, 249480, 201040, 295960, 264684, 346696, 314272, 454608, 352520, 518336, 452256, 591934, 517216 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.

LINKS

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

FORMULA

G.f.: (theta_3(q^(1/2))^7 + theta_4(q^(1/2))^7)/2.

EXAMPLE

1 + 84*q^2 + 574*q^4 + 1288*q^6 + 3444*q^8 + ...

MATHEMATICA

terms = 34; s = 1/2 (EllipticTheta[3, 0, q]^7 + EllipticTheta[4, 0, q]^7) + O[q]^(2 terms); CoefficientList[s, q^2] (* Jean-Fran├žois Alcover, Jul 07 2017 *)

PROG

(PARI) {a(n)=if(n<0, 0, n*=2; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^7, n))} /* Michael Somos, Nov 03 2006 */

CROSSREFS

A008451(2n) = a(n).

Sequence in context: A211260 A233053 A220203 * A175813 A238523 A238518

Adjacent sequences:  A008426 A008427 A008428 * A008430 A008431 A008432

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified January 17 16:11 EST 2019. Contains 319235 sequences. (Running on oeis4.)