A029817 Average theta series of odd unimodular lattices of dimension 16 (multiplied by 17).

17, 32, 4064, 70016, 528352, 2500032, 8892032, 26353408, 67637216, 153125024, 317504064, 623589504, 1156034176, 2007952576, 3346882816, 5470070016, 8657571808, 13130837568, 19446878048, 28603895680, 41278028352, 57661256704, 79195867008, 108954414336, 147990228608

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Heng Huat Chan and Christian Krattenthaler, Recent progress in the study of representations of integers as sums of squares, Bulletin of the London Mathematical Society, Vol. 37, No. 6 (2005), pp. 818-826; arXiv preprint, arXiv:math/0407061 [math.NT], 2004.

Crossrefs

Cf. A013955, A321811.

Programs

Mathematica

max = 20; s = 17 + 32*Sum[k^7*q^k/(1-(-q)^k), {k, 1, max}] + O[q]^max; CoefficientList[s, q] (* Jean-François Alcover, Dec 07 2015 *)

PARI

a(n)=if(n<1,17*(n==0),32*sumdiv(n,d,d^7-2*if(d%4==2,(d/2)^7))) /* Michael Somos, Jul 16 2004 */

Formula

G.f.: 17 + 32 * Sum_{k >= 1} k^7*q^k/(1-(-q)^k).

a(n) = 32 * (-1)^n * (A013955(n) - 2 * A321811(2*n)) for n >= 1. - Amiram Eldar, Jan 07 2025