OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
S. Ahlgren, The sixth, eighth, ninth and tenth powers of Ramanujan's theta function, Proc. Amer. Math. Soc. 128 (2000), 1333-1338.
FORMULA
Empirical g.f.: x*(x^3+3*x^2+5*x+7) / (x^5-x^4-x+1). - Colin Barker, Jul 31 2013
Conjecture: a(n) = 4*n + pa(n mod 4), where pa(k) = 0,3,4,3 for k=0,1,2,3 respectively; lim_{n->infinity} a(n)/n = 4; a(n)/n >= 4; a(n+4) = a(n) + 16. - Jerzy R Borysowicz, Jan 16 2022
MATHEMATICA
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[8, q_]:= ( f[q^4, q^4]^7 + (2*q*f[q^8, q^24])^7 + 14*f[q^2, q^2]^2*f[q^4, q^4]^5 - 7*f[q^4, q^4]^3*f[q^2, q^2]^4)/8; 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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 25 2002
EXTENSIONS
Terms a(25) onward added by G. C. Greubel, Apr 16 2018
STATUS
approved