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%I #48 Sep 08 2022 08:44:46
%S 3,12,15,27,42,69,111,180,291,471,762,1233,1995,3228,5223,8451,13674,
%T 22125,35799,57924,93723,151647,245370,397017,642387,1039404,1681791,
%U 2721195,4402986,7124181,11527167,18651348,30178515,48829863,79008378
%N Fibonacci sequence beginning 3, 12.
%H Indranil Ghosh, <a href="/A022380/b022380.txt">Table of n, a(n) for n = 0..4771</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F G.f.: (3+9*x)/(1-x-x^2). - _Philippe Deléham_, Nov 19 2008
%F a(n) = ((2^(-n-1)/5)*((15+21*sqrt(5))*(1+sqrt(5))^n + (15-21*sqrt(5))*(1-sqrt(5))^n). - _Bogart B. Strauss_, Oct 27 2013
%F a(n) = -(3/2)*(A000045(n+1)-3*A000032(n+1)). - _Harvey P. Dale_, Aug 22 2019
%F a(n) = 3*A000285(n). - _R. J. Mathar_, Jan 08 2020
%t a[0]=3; a[1] = 12; a[n_]:= a[n-1] + a[n-2]; Table[a[n],{n,0,30}] (* or *) LinearRecurrence[{1,1},{3,12},31] (* _Indranil Ghosh_, Feb 19 2017 *)
%t Table[-(3/2)(Fibonacci[n]-3*LucasL[ n]),{n,40}] (* _Harvey P. Dale_, Aug 22 2019 *)
%o (Magma) [-(3/2)*(Fibonacci(n+1)-3*Lucas(n+1)): n in [0..40]]; // _Vincenzo Librandi_, Jan 09 2020
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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