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%I #21 Sep 08 2022 08:44:36
%S 1,2,3,4,6,8,10,13,16,19,22,26,30,34,39,44,49,54,60,66,72,79,86,93,
%T 100,108,116,124,133,142,151,160,170,180,190,201,212,223,234,246,258,
%U 270,283,296,309,322,336,350,364,379,394,409,424,440,456,472,489
%N Molien series for 3-dimensional group [2+,n] = 2*(n/2).
%H Vincenzo Librandi, <a href="/A008739/b008739.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_09">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,1,-2,1).
%F G.f.: (1+x^4)/((1-x)^2*(1-x^7)).
%t LinearRecurrence[{2,-1,0,0,0,0,1,-2,1},{1,2,3,4,6,8,10,13,16},50] (* _Harvey P. Dale_, May 05 2017 *)
%t CoefficientList[Series[(1+x^4)/(1-x)^2/(1-x^7), {x,0,50}], x] (* _Vincenzo Librandi_, May 06 2017 *)
%o (Magma) I:=[1,2,3,4,6,8,10,13,16]; [n le 9 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-7)-2*Self(n-8)+Self(n-9): n in [1..50]]; // _Vincenzo Librandi_, May 06 2017
%o (PARI) my(x='x+O('x^50)); Vec((1+x^4)/((1-x)^2*(1-x^7))) \\ _G. C. Greubel_, Aug 03 2019
%o (Sage) ((1+x^4)/((1-x)^2*(1-x^7))).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 03 2019
%o (GAP) a:=[1,2,3,4,6,8,10,13,16];; for n in [10..50] do a[n]:=2*a[n-1] -a[n-2]+a[n-7]-2*a[n-8]+a[n-9]; od; a; # _G. C. Greubel_, Aug 03 2019
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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