OFFSET
0,2
COMMENTS
The exponents occurring in the expansion of F_6(q^2) (see Ahlgren) or, equivalently, the norms of the vectors in the A*_5 lattice. - Andrey Zabolotskiy, Oct 26 2024
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Scott Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc. 128 (2000), 1333-1338.
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).
FORMULA
G.f.: x*(3*x^2-2*x+5) / ((x-1)^2*(x^2+1)). - Colin Barker, Jul 31 2013
Sum_{n>=1} 1/a(n) = Pi*(3-2*sqrt(3))/72 + log(2)/2 - arccoth(sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Jul 26 2024
E.g.f.: exp(x)*(1 + 3*x) - cos(x) + sin(x). - Stefano Spezia, Oct 27 2024
MATHEMATICA
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[6, q_]:= ( -3*f[q, q]^5 + 5*f[q, q]^3*f[q^3, q^3]^2 + 15*f[q, q]*f[q^3, q^3]^4 + 15*f[q^3, q^3]^6/f[q, q] )/32; cfs = CoefficientList[Series[F[6, q], {q, 0, 500}], q]; Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* G. C. Greubel, Apr 16 2018 *)
Flatten[#+{0, 5, 8, 9}&/@(12*Range[0, 20])] (* Harvey P. Dale, Apr 10 2022 *)
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Jul 25 2002
EXTENSIONS
Terms a(33) onward added by G. C. Greubel, Apr 16 2018
Edited by Andrey Zabolotskiy, Aug 14 2020
STATUS
approved