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%I #34 Sep 08 2022 08:45:14
%S 1,1,1,2,2,3,4,4,5,6,7,8,9,10,11,13,14,15,17,18,21,23,24,27,29,32,35,
%T 37,40,43,47,50,53,57,60,65,69,72,77,81,86,91,95,100,105,111,116,121,
%U 127,132,139,145,150,157,163,170,177,183,190,197,205,212,219,227,234,243,251,258
%N Expansion of (1+x^20)/((1-x)*(1-x^3)*(1-x^5)).
%D G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 191, Cor. 2.2.
%H G. C. Greubel, <a href="/A097923/b097923.txt">Table of n, a(n) for n = 0..1000</a>
%H G. van der Geer, <a href="https://doi.org/10.1007/978-3-642-61553-5">Hilbert Modular Surfaces</a>, in: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 16, Springer-Verlag (1988).
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,-1,0,-1,1).
%F G.f.: (1+x^20)/((1-x)*(1-x^3)*(1-x^5)).
%t CoefficientList[Series[(1 + x^20)/((1 - x)*(1 - x^3)*(1 - x^5)), {x, 0, 100}], x] (* _Wesley Ivan Hurt_, Mar 30 2017 *)
%t LinearRecurrence[{1,0,1,-1,1,-1,0,-1,1},{1,1,1,2,2,3,4,4,5,6,7,8,9,10,11,13,14,15,17,18,21}, 68] (* _G. C. Greubel_, Dec 20 2017; more initial terms by _Georg Fischer_, Apr 08 2019 *)
%o (PARI) x='x+O('x^30); Vec((1+x^20)/((1-x)*(1-x^3)*(1-x^5))) \\ _G. C. Greubel_, Dec 20 2017
%o (Magma) I:=[1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 21];
%o [n le 21 select I[n] else Self(n-1) + Self(n-3) - Self(n-4) + Self(n-5) - Self(n-6) - Self(n-8) + Self(n-9): n in [1..80]]; // _G. C. Greubel_, Dec 20 2017; more initial terms by _Georg Fischer_, Apr 03 2019
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_, Sep 05 2004
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