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 are all in this list and probably include all numbers in this list. - Andrey Zabolotskiy, Aug 14 2020
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
MATHEMATICA
(* This program is based on the function F_6(q^2), so it is not proved that it generates all terms. *) 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
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