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%I #17 Sep 08 2022 08:45:08
%S 1,1,0,1,3,2,1,5,8,5,7,18,21,17,32,57,59,66,121,173,184,253,415,530,
%T 621,921,1360,1681,2163,3202,4401,5525,7528,10805,14327,18578,25861,
%U 35937,47232,63017,87659,119106,157481,213693,294424,395693,528655,721810,984541,1320041
%N Expansion of 1/(1-x+x^2-2*x^3).
%H Vincenzo Librandi, <a href="/A077951/b077951.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).
%t LinearRecurrence[{1, -1, 2}, {1, 1, 0}, 60] (* _Vladimir Joseph Stephan Orlovsky_, Feb 23 2012 *)
%t CoefficientList[Series[1/(1-x+x^2-2*x^3), {x,0,50}], x] (* _G. C. Greubel_, Jul 03 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_, Jul 03 2019
%o (Sage) (1/(1-x+x^2-2*x^3)).series(x, 50).coefficients(x, sparse=False) # _G. C. Greubel_, Jul 03 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_, Jul 03 2019
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_, Nov 17 2002
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