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%I #31 Sep 08 2022 08:44:36
%S 1,2,3,4,5,6,7,8,9,10,12,14,16,18,20,22,24,26,28,30,33,36,39,42,45,48,
%T 51,54,57,60,64,68,72,76,80,84,88,92,96,100,105,110,115,120,125,130,
%U 135,140,145,150,156,162,168,174,180,186,192,198,204,210,217,224,231,238
%N Molien series for 3-dimensional group [2,n ] = *22n.
%C a(n) = A179052(n) for n < 100. - _Reinhard Zumkeller_, Jun 27 2010
%H Vincenzo Librandi, <a href="/A008728/b008728.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=193">Encyclopedia of Combinatorial Structures 193</a>
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).
%F G.f.: 1/((1-x)^2*(1-x^10)).
%F From _Mitch Harris_, Sep 08 2008: (Start)
%F a(n) = Sum_{j=0..n+10} floor(j/10).
%F a(n-10) = (1/2)*floor(n/10)*(2*n - 8 - 10*floor(n/10)). (End)
%p g:= 1/((1-x)^2*(1-x^10)); gser:= series(g, x=0,72); seq(coeff(gser, x, n), n=0..70); # modified by _G. C. Greubel_, Jul 30 2019
%t CoefficientList[Series[1/((1-x)^2(1-x^10)), {x,0,70}], x] (* _Vincenzo Librandi_, Jun 11 2013 *)
%o (PARI) my(x='x+O('x^70)); Vec(1/((1-x)^2*(1-x^10))) \\ _G. C. Greubel_, Jul 30 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)^2*(1-x^10)) )); // _G. C. Greubel_, Jul 30 2019
%o (Sage) (1/((1-x)^2*(1-x^10))).series(x, 70).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 30 2019
%o (GAP) a:=[1,2,3,4,5,6,7,8,9,10,12,14];; for n in [13..70] do a[n]:=2*a[n-1]-a[n-2]+a[n-10]-2*a[n-11]+a[n-12]; od; a; # _G. C. Greubel_, Jul 30 2019
%Y Cf. A001840, A001972, A008724, A008725, A008726, A008727, A008732.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Vladimir Joseph Stephan Orlovsky_, Mar 14 2010
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