The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A008429 Theta series of D_7 lattice. 3

%I

%S 1,84,574,1288,3444,4424,9240,11088,18494,19740,34440,31304,52808,

%T 52248,74048,71120,110964,94864,145222,132888,181384,163856,249480,

%U 201040,295960,264684,346696,314272,454608,352520,518336,452256,591934,517216

%N Theta series of D_7 lattice.

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

%H Seiichi Manyama, <a href="/A008429/b008429.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%t 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 *)

%o (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 */

%Y A008451(2n) = a(n).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 4 11:28 EST 2021. Contains 349486 sequences. (Running on oeis4.)