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%I #39 Apr 06 2023 08:33:31
%S 0,1,9,84,783,7299,68040,634257,5912433,55114668,513769311,4789267803,
%T 44644718160,416170266849,3879466556121,36163709805636,
%U 337111787919087,3142497220688691,29293810349955480,273071784811665393,2545527494354854977,23728962803628690972
%N a(n) = 9*a(n-1) + 3*a(n-2); a(0) = 0, a(1) = 1.
%H G. C. Greubel, <a href="/A181353/b181353.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 (9,3).
%F a(n) = ((9+sqrt(93))^n - (9-sqrt(93))^n)/(2^n*sqrt(93)). - _Rolf Pleisch_, May 14 2011
%F G.f.: x/(1 - 9*x - 3*x^2). - _Philippe Deléham_, Nov 21 2011
%F a(n+1) = Sum_{k=0..n} A099097(n,k)*3^k. - _Philippe Deléham_, Nov 21 2011
%F E.g.f.: 2*exp(9*x/2)*sinh(sqrt(93)*x/2)/sqrt(93). - _Stefano Spezia_, Apr 06 2023
%t Join[{a=0,b=1},Table[c=9*b+3*a;a=b;b=c,{n,60}]]
%t LinearRecurrence[{9,3}, {0,1}, 30] (* _G. C. Greubel_, Jan 24 2018 *)
%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-9*x-3*x^2))) \\ _G. C. Greubel_, Jan 24 2018
%o (Magma) I:=[0,1]; [n le 2 select I[n] else 9*Self(n-1) + 3*Self(n-2): n in [1..30]];
%Y Cf. A015579, A099371.
%K nonn,easy
%O 0,3
%A _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011
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