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%I #30 Jan 11 2024 03:30:51
%S 0,1,3,0,-27,-81,0,729,2187,0,-19683,-59049,0,531441,1594323,0,
%T -14348907,-43046721,0,387420489,1162261467,0,-10460353203,
%U -31381059609,0,282429536481,847288609443,0,-7625597484987,-22876792454961,0,205891132094649
%N a(n) = 3*a(n-1) - 9*a(n-2), with a(0)=0, a(1)=1.
%H G. C. Greubel, <a href="/A190963/b190963.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-9).
%F G.f.: x/(1-3*x+9*x^2). - _Philippe Deléham_, Oct 11 2011
%F From _G. C. Greubel_, Jan 11 2024: (Start)
%F a(n) = 3^(n-1)*ChebyshevU(n-1, 1/2).
%F a(n) = 3^(n-1)*A128834(n).
%F E.g.f.: (2/(3*sqrt(3)))*exp(3*x/2)*sin(3*sqrt(3)*x/2). (End)
%t LinearRecurrence[{3,-9}, {0,1}, 50]
%o (PARI) my(x='x+O('x^30)); concat([0], Vec(x/(1-3*x+9*x^2))) \\ _G. C. Greubel_, Jan 25 2018
%o (Magma) [n le 2 select n-1 else 3*Self(n-1)-9*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 25 2018
%o (SageMath)
%o A190963=BinaryRecurrenceSequence(3,-9,0,1)
%o [A190963(n) for n in range(41)] # _G. C. Greubel_, Jan 11 2024
%Y Cf. A190958 (index to generalized Fibonacci sequences).
%Y Cf. A128834.
%K sign,easy
%O 0,3
%A _Vladimir Joseph Stephan Orlovsky_, May 24 2011