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%I #43 Sep 08 2022 08:44:36
%S 1,2,3,4,5,7,9,11,13,16,19,22,25,28,32,36,40,44,49,54,59,64,69,75,81,
%T 87,93,100,107,114,121,128,136,144,152,160,169,178,187,196,205,215,
%U 225,235,245,256,267,278,289,300,312,324,336,348,361,374,387,400,413,427,441,455,469,484
%N Molien series for 3-dimensional group [2+,n] = 2*(n/2).
%H G. C. Greubel, <a href="/A008740/b008740.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_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
%F G.f.: (1+x^5)/((1-x)^2*(1-x^9)).
%F Nearest integer to (n+3)^2/9. [Corrected by _Gerald Hillier_, Dec 24 2017]
%F a(n) = a(n-4) + n. - _Paul Barry_, Jul 14 2004
%F a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11).
%F a(n) = floor((n^2 + 6*n + 12)/9). - _Tani Akinari_, Aug 19 2013
%t CoefficientList[Series[(1+x^5)/((1-x)^2(1-x^9)),{x,0,70}],x] (* _Harvey P. Dale_, Aug 27 2011 *)
%t Floor[((Range[0,70]+3)^2 + 3)/9] (* _G. C. Greubel_, Aug 03 2019 *)
%o (PARI) vector(70, n, n--; ((n+3)^2+3)\9) \\ _G. C. Greubel_, Aug 03 2019
%o (Magma) [Floor((n+3)^2+3)/9: n in [0..70]]; // _G. C. Greubel_, Aug 03 2019
%o (Sage) [floor((n+3)^2+3)/9 for n in (0..70)] # _G. C. Greubel_, Aug 03 2019
%o (GAP) List([0..70], n-> Int(((n+3)^2+3)/9)); # _G. C. Greubel_, Aug 03 2019
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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