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%I #39 Sep 08 2022 08:44:46
%S 3,9,12,21,33,54,87,141,228,369,597,966,1563,2529,4092,6621,10713,
%T 17334,28047,45381,73428,118809,192237,311046,503283,814329,1317612,
%U 2131941,3449553,5581494,9031047,14612541,23643588,38256129,61899717,100155846,162055563,262211409
%N Fibonacci sequence beginning 3, 9.
%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 + 6*x)/(1 - x - x^2). - _Philippe Deléham_, Nov 19 2008
%F a(n+2) = 3*L(n+3) = L(n) + 4*L(n+1) + 2*L(n+2), where L=A000032. - _J. M. Bergot_, Oct 21 2012
%F a(n) = Fibonacci(n+4) - Fibonacci(n-4), where n>0 and Fibonacci(-3..-1) = 2,-1,1. - _Bruno Berselli_, May 22 2015
%F a(n) = L(n+4) + L(n-4) - 4*L(n) for n>0. - _Bruno Berselli_, Dec 29 2016
%t LinearRecurrence[{1, 1}, {3, 9}, 30] (* _Alonso del Arte_, Oct 09 2013 *)
%t Table[3 LucasL[n + 1], {n, 0, 40}] (* _Bruno Berselli_, May 22 2015 *)
%t Table[LucasL[n + 4] + LucasL[n - 4] - 4 LucasL[n], {n, 1, 40}] (* _Bruno Berselli_, Dec 30 2016 *)
%o (PARI) Vec((3+6*x)/(1-x-x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Oct 21 2012
%o (Magma) [3*Lucas(n+1): n in [0..40]]; // _Bruno Berselli_, May 22 2015
%Y Cf. A000032, A000045.
%Y Cf. similar sequences listed in A258160.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
%E More terms from _Bruno Berselli_, May 22 2015
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