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%I #17 Sep 08 2022 08:44:36
%S 1,1,2,3,4,5,7,8,10,12,15,17,21,24,28,32,37,41,47,52,58,64,71,77,85,
%T 92,100,108,117,125,135,144,154,164,175,185,197,208,220,232,245,257,
%U 271,284,298,312,327,341
%N Expansion of (1+x^10)/((1-x)*(1-x^2)*(1-x^3)).
%H G. C. Greubel, <a href="/A008753/b008753.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F a(n) = (6*(n-2)^2 + 143 + 4*cos(2*n*Pi/3) + 4*sqrt(3)*sin(2*n*Pi/3) + 9*(-1)^n)/36 for n >= 5. - _G. C. Greubel_, Aug 04 2019
%t CoefficientList[Series[(1+x^10)/(1-x)/(1-x^2)/(1-x^3),{x,0,60}],x] (* _Harvey P. Dale_, Jan 30 2013 *)
%t Join[{1,1,2,3,4}, Table[(6*(n-2)^2 +143 +4*Cos[2*n*Pi/3] + 4*Sqrt[3]* Sin[2*n*Pi/3] +9*(-1)^n)/36, {n,5,60}]] (* _G. C. Greubel_, Aug 04 2019 *)
%o (PARI) my(x='x+O('x^60)); Vec((1+x^10)/((1-x)*(1-x^2)*(1-x^3))) \\ _G. C. Greubel_, Aug 04 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^10)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 04 2019
%o (Sage) ((1+x^10)/((1-x)*(1-x^2)*(1-x^3))).series(x, 60).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 04 2019
%o (GAP) a:=[7,8,10,12,15,17];; for n in [7..60] do a[n]:=a[n-1]+a[n-2]-a[n-4] -a[n-5]+a[n-6]; od; Concatenation([1,1,2,3,4,5], a); # _G. C. Greubel_, Aug 04 2019
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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