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%I #14 Sep 08 2022 08:45:14
%S 1,1,3,4,6,9,12,16,21,26,32,39,46,54,63,72,82,93,104,116,129,142,156,
%T 171,186,202,219,236,254,273,292,312,333,354,376,399,422,446,471,496,
%U 522,549,576,604,633,662,692,723,754,786,819,852,886,921,956,992,1029,1066,1104
%N G.f.: (1-x^4)*(1-x^10)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^5)).
%D G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 188.
%H G. C. Greubel, <a href="/A097922/b097922.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 + ceiling((n^2 - n)/3) for n >= 2. - _Robert Israel_, May 20 2014
%t CoefficientList[Series[(1-x^4)*(1-x^10)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^5)), {x,0,50}], x] (* or *) Join[{1,1}, LinearRecurrence[{2,-1,1,-2, 1}, {3, 4, 6, 9, 12}, 30]] (* or *) Join[{1,1}, Table[2 + Ceiling[n*(n-1)/3], {n,2,30}]] (* _G. C. Greubel_, Dec 20 2017 *)
%o (PARI) x='x+O('x^30); Vec((1-x^4)*(1-x^10)/((1-x)*(1-x^2)^2*(1-x^3)*(1-x^5))) \\ _G. C. Greubel_, Dec 20 2017
%o (PARI) for(n=0,30, print1(if(n==0, 1, if(n==1, 1, 2 + ceil(n*(n-1)/3))), ", ")) \\ _G. C. Greubel_, Dec 20 2017
%o (Magma) [1,1] cat [2 + Ceiling(n*(n-1)/3): n in [2..30]]; // _G. C. Greubel_, Dec 20 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Sep 05 2004
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