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%I #20 Sep 08 2022 08:45:14
%S 1,1,2,4,6,8,12,16,20,26,32,38,46,54,62,72,82,92,104,116,128,142,156,
%T 170,186,202,218,236,254,272,292,312,332,354,376,398,422,446,470,496,
%U 522,548,576,604,632,662,692,722,754,786,818,852,886,920,956,992,1028,1066,1104
%N G.f.: (1-x^6)*(1-x^8)/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)).
%D G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 188.
%H Vincenzo Librandi, <a href="/A097921/b097921.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).
%F a(n) = 2 + floor(n*(n - 1)/3), for n>=2, with a(0)=1, a(1)=1. - _G. C. Greubel_, Dec 20 2017
%t CoefficientList[Series[(1 - x^6) (1 - x^8)/((1 - x) (1 - x^2) (1 - x^3)^2 (1 - x^4)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 29 2014 *)
%t Join[{1,1}, LinearRecurrence[{2,-1,1,-2, 1}, {2, 4, 6, 8, 12}, 30]] (* or *) Join[{1,1}, Table[2 + Floor[n*(n-1)/3], {n,2,30}]] (* _G. C. Greubel_, Dec 20 2017 *)
%o (PARI) a(n)=n*(n-1)\3+2-(n<2) \\ _Tani Akinari_, Jun 27 2014
%o (PARI) Vec((1-x^6)*(1-x^8)/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)) + O(x^100)) \\ _Michel Marcus_, Jun 28 2014
%o (PARI) for(n=0,30, print1(if(n==0, 1, if(n==1, 1, 2 + floor(n*(n-1)/3))), ", ")) \\ _G. C. Greubel_, Dec 20 2017
%o (Magma) [1,1] cat [2 + Floor(n*(n-1)/3): n in [2..30]]; // _G. C. Greubel_, Dec 20 2017
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Sep 05 2004
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