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%I #13 Sep 08 2022 08:45:28
%S 1,2,6,14,46,102,358,734,2814,5174,22390,35310,180814,228230,1486086,
%T 1330814,12461854,6032982,106833430,4449422,937368942,-387288922,
%U 8418522790,-7235076066,77315860798,-98789775754,724783051446,-1198371424978,6918206566030,-13684475030586
%N a(n) = 9*a(n-2) - 4*a(n-3) for n > 2 with a(0)=1, a(1)=2.
%H G. C. Greubel, <a href="/A122109/b122109.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 (0,9,-4).
%F G.f.: (1 + 2*x - 3*x^2)/(1 - 9*x^2 + 4*x^3).
%p seq(coeff(series((1+2*x-3*x^2)/(1-9*x^2+4*x^3), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Oct 02 2019
%t LinearRecurrence[{0,9,-4}, {1,2,6}, 30] (* _G. C. Greubel_, Oct 02 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((1+2*x-3*x^2)/(1-9*x^2+4*x^3)) \\ _G. C. Greubel_, Oct 02 2019
%o (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+2*x-3*x^2)/(1-9*x^2+4*x^3) )); // _G. C. Greubel_, Oct 02 2019
%o (Sage)
%o def A122109_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P((1+2*x-3*x^2)/(1-9*x^2+4*x^3)).list()
%o A122109_list(30) # _G. C. Greubel_, Oct 02 2019
%o (GAP) a:=[1,2,6];; for n in [4..30] do a[n]:=9*a[n-2]-4*a[n-3]; od; a; # _G. C. Greubel_, Oct 02 2019
%K sign
%O 0,2
%A _Philippe Deléham_, Oct 18 2006
%E Terms a(26) onward added by _G. C. Greubel_, Oct 02 2019
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