A072835 Exponents occurring in expansion of F_9(q^2).
0, 8, 14, 18, 20, 26, 32, 36, 38, 44, 50, 54, 56, 62, 68, 72, 74, 80, 86, 90, 92, 98, 104, 108, 110, 116, 122, 126, 128, 134, 140, 144, 146, 152, 158, 162, 164, 170, 176, 180, 182, 188, 194, 198, 200, 206, 212, 216, 218, 224, 230, 234, 236, 242, 248, 252, 254, 260, 266, 270, 272, 278
Offset: 0
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.
- Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
Crossrefs
Programs
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Mathematica
f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y]; F[9,q_]:= f[q^9, q^9]^8 - 16*q^9*f[q^9, q^27]^8 + 256*q^18*f[q^18, q^54]^8 + 18*q^8*QPochhammer[q^18]^12/QPochhammer[q^6]^4; cfs = CoefficientList[Series[F[9, q], {q, 0, 500}], q]; Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* G. C. Greubel, Apr 16 2018 *)
Formula
G.f.: -2*x*(x^4-x^3-2*x^2-3*x-4) / (x^5-x^4-x+1). - Colin Barker, Jul 31 2013
a(n+4) = a(n) + 18 for n > 0. - Jerzy R Borysowicz, Sep 02 2023
a(n)/n ~ 9/2. - Jerzy R Borysowicz, Sep 03 2023
a(n) = 2 * A056991(n+1) for n>=1. - Alois P. Heinz, Sep 03 2023
Extensions
Terms a(22) onward added by G. C. Greubel, Apr 16 2018
Comments