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A136297 a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3), with a(0)=1, a(1)=3, a(2)=1.

%I A136297 #13 Apr 13 2021 01:36:23
%S A136297 1,3,1,-3,-3,3,9,9,9,27,81,189,405,891,2025,4617,10449,23571,53217,
%T A136297 120285,271917,614547,1388745,3138345,7092441,16028523,36223281,
%U A136297 81861597,185000517,418086603,944843049,2135270889,4825543329,10905346467,24645222081,55696256829,125869143645
%N A136297 a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3), with a(0)=1, a(1)=3, a(2)=1.
%H A136297 Harvey P. Dale, <a href="/A136297/b136297.txt">Table of n, a(n) for n = 0..1000</a>
%H A136297 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3).
%F A136297 From _R. J. Mathar_, Apr 04 2008: (Start)
%F A136297 O.g.f.: (1 -5*x^2)/(1 -3*x +3*x^2 -3*x^3).
%F A136297 a(n) = A052103(n+1) - 5*A052103(n-1). (End)
%p A136297 m:=40; S:=series( (1-5*x^2)/(1-3*x+3*x^2-3*x^3), x, m+1): seq(coeff(S, x, j), j=0..m); # _G. C. Greubel_, Apr 12 2021
%t A136297 LinearRecurrence[{3,-3,3},{1,3,1},40] (* _Harvey P. Dale_, Jun 22 2013 *)
%o A136297 (Magma) I:=[1,3,1]; [n le 3 select I[n] else 3*(Self(n-1) -Self(n-2) +Self(n-3)): n in [1..41]]; // _G. C. Greubel_, Apr 12 2021
%o A136297 (Sage)
%o A136297 def A136297_list(prec):
%o A136297     P.<x> = PowerSeriesRing(ZZ, prec)
%o A136297     return P( (1-5*x^2)/(1-3*x+3*x^2-3*x^3) ).list()
%o A136297 A136297_list(40) # _G. C. Greubel_, Apr 12 2021
%Y A136297 Cf. A052103.
%K A136297 sign,easy
%O A136297 0,2
%A A136297 _Paul Curtz_, Mar 21 2008
%E A136297 More terms from _R. J. Mathar_, Apr 04 2008