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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
OFFSET
0,2
REFERENCES
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 118.
LINKS
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-François 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
KEYWORD
nonn,easy
STATUS
approved