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Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)).
1

%I #14 Sep 08 2022 08:44:36

%S 1,1,2,3,4,5,7,8,10,13,15,18,22,25,29,34,38,43,49,54,60,67,73,80,88,

%T 95,103,112,120,129,139,148,158,169,179,190,202,213,225,238,250,263,

%U 277,290,304,319,333,348

%N Expansion of (1+x^9)/((1-x)*(1-x^2)*(1-x^3)).

%H G. C. Greubel, <a href="/A008752/b008752.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

%t CoefficientList[Series[(1+x^9)/((1-x)*(1-x^2)*(1-x^3)), {x, 0, 50}], x] (* _G. C. Greubel_, Aug 04 2019 *)

%t LinearRecurrence[{2,-1,1,-2,1},{1,1,2,3,4,5,7,8,10},50] (* _Harvey P. Dale_, Oct 24 2020 *)

%o (PARI) my(x='x+O('x^50)); Vec((1+x^9)/((1-x)*(1-x^2)*(1-x^3))) \\ _G. C. Greubel_, Aug 04 2019

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^9)/((1-x)*(1-x^2)*(1-x^3)) )); // _G. C. Greubel_, Aug 04 2019

%o (Sage) ((1+x^9)/((1-x)*(1-x^2)*(1-x^3))).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 04 2019

%o (GAP) a:=[1,1,2,3,4];; for n in [6..50] do a[n]:=2*a[n-1]-a[n-2]+a[n-3] -2*a[n-4]+a[n-5]; od; a; # _G. C. Greubel_, Aug 04 2019

%K nonn

%O 0,3

%A _N. J. A. Sloane_