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%I #17 Sep 08 2022 08:45:08
%S 1,0,2,4,8,20,44,100,228,516,1172,2660,6036,13700,31092,70564,160148,
%T 363460,824884,1872100,4248788,9642756,21884532,49667620,112722196,
%U 255826500,580606132,1317703524,2990568788,6787188100,15403732724,34959246500,79341088148,180067046596
%N Expansion of (1-x)/(1-x-2*x^2-2*x^3).
%H Harvey P. Dale, <a href="/A078006/b078006.txt">Table of n, a(n) for n = 0..999</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 2, 2).
%F a(0)=1, a(1)=0, a(2)=2, a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3). - _Harvey P. Dale_, Sep 25 2011
%t CoefficientList[Series[(1-x)/(1-x-2x^2-2x^3),{x,0,40}],x] (* or *) LinearRecurrence[{1,2,2},{1,0,2},41] (* _Harvey P. Dale_, Sep 25 2011 *)
%o (PARI) Vec((1-x)/(1-x-2*x^2-2*x^3)+O(x^40)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1-x)/(1-x-2*x^2-2*x^3) )); // _G. C. Greubel_, Jun 27 2019
%o (Sage) ((1-x)/(1-x-2*x^2-2*x^3)).series(x, 40).coefficients(x, sparse=False) # _G. C. Greubel_, Jun 27 2019
%o (GAP) a:=[1,0,2];; for n in [4..40] do a[n]:=a[n-1]+2*a[n-2]+2*a[n-3]; od; a; # _G. C. Greubel_, Jun 27 2019
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Nov 17 2002
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