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%I #23 Sep 08 2022 08:45:08
%S 1,1,0,-3,-5,-2,9,21,16,-23,-81,-90,37,289,432,69,-941,-1874,-1071,
%T 2685,7504,6961,-5913,-27882,-35891,3817,95472,163437,60331,-294050,
%U -681255,-507867,761488,2631865,2886111,-1268730,-9418571,-13922063,-1966032,30793173,60603331,33742222,-88447455
%N Expansion of 1/(1 - x + x^2 + 2*x^3).
%C Row sums of Riordan array (1, x*(1-x-2*x^2)). - _Paul Barry_, Mar 09 2006
%H G. C. Greubel, <a href="/A077952/b077952.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,-2).
%F a(n) = Sum_{k=0..n} Sum_{j=0..n} C(k,j-k)*C(k,n-j)*(-2)^(n-j). - _Paul Barry_, Mar 09 2006
%F a(n) = (-1)^n*A077975(n). - _R. J. Mathar_, Jul 31 2010
%p seq(coeff(series(1/(1-x+x^2+2*x^3), x, n+1), x, n), n = 0 .. 50); # _G. C. Greubel_, Aug 07 2019
%t LinearRecurrence[{1,-1,-2}, {1,1,0}, 50] (* or *) CoefficientList[Series[ 1/(1-x+x^2+2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Aug 07 2019 *)
%o (PARI) Vec(1/(1-x+x^2+2*x^3)+O(x^50)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( 1/(1-x+x^2+2*x^3) )); // _G. C. Greubel_, Aug 07 2019
%o (Sage) (1/(1-x+x^2+2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 07 2019
%o (GAP) a:=[1,1,0];; for n in [4..50] do a[n]:=a[n-1]-a[n-2]-2*a[n-3]; od; a; # _G. C. Greubel_, Aug 07 2019
%K sign,easy
%O 0,4
%A _N. J. A. Sloane_, Nov 17 2002
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