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%I #26 Sep 08 2022 08:45:49
%S 0,9,36,117,360,1089,3276,9837,29520,88569,265716,797157,2391480,
%T 7174449,21523356,64570077,193710240,581130729,1743392196,5230176597,
%U 15690529800,47071589409,141214768236,423644304717,1270932914160
%N a(n) = 9*(3^n - 1)/2.
%H Vincenzo Librandi, <a href="/A168569/b168569.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 (4,-3).
%F From _R. J. Mathar_, Jan 04 2011: (Start)
%F a(n) = 9*A003462(n).
%F G.f.: 9*x / ( (3*x-1)*(x-1) ). (End)
%F a(n) = 4*a(n-1)-3*a(n-2). - _Robert Israel_, Sep 24 2014
%F E.g.f.: (9/2)*(exp(3*x) - exp(x)). - _G. C. Greubel_, Jul 26 2016
%t 9 (3^Range[0,30]-1)/2 (* _Harvey P. Dale_, Mar 18 2011 *)
%t CoefficientList[Series[9 x / ((1 - x) (1 - 3 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Sep 24 2014 *)
%o (Magma) [9*(3^n-1)/2: n in [0..30]]; // _Vincenzo Librandi_, Sep 24 2014
%o (PARI) a(n)=9*(3^n-1)/2 \\ _Charles R Greathouse IV_, Jul 26 2016
%Y Cf. A003462.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Nov 30 2009
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