OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..5000 from G. C. Greubel)
J. H. Conway and N. J. A. Sloane, Sphere Packings, Lattices and Groups, Springer-Verlag, p. 118.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, arXiv:math/0509316 [math.NT], 2005-2006.
N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
FORMULA
G.f.: (theta_3(q^(1/2))^8 + theta_4(q^(1/2))^8)/2.
a(n) = A000143(2n).
EXAMPLE
1 + 112*q^2 + 1136*q^4 + 3136*q^6 + 9328*q^8 + ...
MATHEMATICA
a[n_] := 16*DivisorSum[n, #^3*(8 - Mod[#, 2]) &]; a[0] = 1; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Dec 02 2015, adapted from PARI *)
PROG
(PARI) {a(n)=if(n<1, n==0, 16*sumdiv(n, d, d^3*(8-d%2)))} /* Michael Somos, Nov 03 2006 */
(PARI) {a(n)=if(n<0, 0, n*=2; polcoeff( sum(k=1, sqrtint(n), 2*x^k^2, 1+x*O(x^n))^8, n))} /* Michael Somos, Nov 03 2006 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved