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Expansion of (1+x^18)/((1-x)*(1-x^2)*(1-x^3)).
1

%I #13 Sep 08 2022 08:44:36

%S 1,1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30,33,38,41,46,51,56,61,68,

%T 73,80,87,94,101,110,117,126,135,144,153,164,173,184,195,206,217,230,

%U 241,254,267,280,293,308

%N Expansion of (1+x^18)/((1-x)*(1-x^2)*(1-x^3)).

%H G. C. Greubel, <a href="/A008761/b008761.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).

%p seq(coeff(series((1+x^18)/((1-x)*(1-x^2)*(1-x^3)), x, n+1), x, n), n = 0 .. 40); # _G. C. Greubel_, Aug 09 2019

%t Join[{1,1,2,3,4,5,7,8,10,12,14,16,19}, LinearRecurrence[{1,1,0,-1,-1,1}, {21,24,27,30,33,38}, 47]] (* _G. C. Greubel_, Aug 09 2019 *)

%t CoefficientList[Series[(1+x^18)/((1-x)(1-x^2)(1-x^3)),{x,0,70}],x] (* _Harvey P. Dale_, Jun 06 2021 *)

%o (PARI) my(x='x+O('x^60)); Vec((1+x^18)/((1-x)*(1-x^2)*(1-x^3))) \\ _G. C. Greubel_, Aug 09 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1+x^18)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 09 2019

%o (Sage)

%o def A008761_list(prec):

%o P.<x> = PowerSeriesRing(ZZ, prec)

%o return P((1+x^18)/((1-x)*(1-x^2)*(1-x^3))).list()

%o A008761_list(60) # _G. C. Greubel_, Aug 09 2019

%o (GAP) a:=[21,24,27,30,33,38];; 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([1,1,2,3,4,5,7,8,10,12,14,16, 19], a); # _G. C. Greubel_, Aug 09 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_