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A072835 Exponents occurring in expansion of F_9(q^2).

%I A072835 #47 Oct 03 2023 17:45:22
%S A072835 0,8,14,18,20,26,32,36,38,44,50,54,56,62,68,72,74,80,86,90,92,98,104,
%T A072835 108,110,116,122,126,128,134,140,144,146,152,158,162,164,170,176,180,
%U A072835 182,188,194,198,200,206,212,216,218,224,230,234,236,242,248,252,254,260,266,270,272,278
%N A072835 Exponents occurring in expansion of F_9(q^2).
%C A072835 Twice (A242660 without 1). Also, norms of vectors of the A*_8 lattice. - _Andrey Zabolotskiy_, Nov 10 2021
%H A072835 G. C. Greubel, <a href="/A072835/b072835.txt">Table of n, a(n) for n = 0..1000</a>
%H A072835 S. Ahlgren, <a href="https://doi.org/10.1090/S0002-9939-99-05181-3">The sixth, eighth, ninth and tenth powers of Ramanujan's theta function</a>, Proc. Amer. Math. Soc. 128 (2000), 1333-1338.
%H A072835 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A072835 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
%F A072835 a(n+4) = a(n) + 18 for n > 0. - _Jerzy R Borysowicz_, Sep 02 2023
%F A072835 a(n)/n ~ 9/2. - _Jerzy R Borysowicz_, Sep 03 2023
%F A072835 a(n) = 2 * A056991(n+1) for n>=1. - _Alois P. Heinz_, Sep 03 2023
%t A072835 f[x_, y_]:= QPochhammer[-x, x*y]*QPochhammer[-y, x*y]*QPochhammer[x*y, x*y];
%t A072835 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;
%t A072835 cfs = CoefficientList[Series[F[9, q], {q, 0, 500}], q];
%t A072835 Take[Pick[Range[Length[cfs]] - 1, Sign[Abs[cfs]], 1], 50] (* _G. C. Greubel_, Apr 16 2018 *)
%Y A072835 Cf. A072839, A242660.
%Y A072835 Cf. A004014, A047222, A072833, A047328, A072834, A072836.
%Y A072835 Cf. A056991.
%K A072835 nonn,easy
%O A072835 0,2
%A A072835 _N. J. A. Sloane_, Jul 25 2002
%E A072835 Terms a(22) onward added by _G. C. Greubel_, Apr 16 2018