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%I #53 Dec 18 2023 12:18:31
%S -3,11,-30,79,-207,542,-1419,3715,-9726,25463,-66663,174526,-456915,
%T 1196219,-3131742,8199007,-21465279,56196830,-147125211,385178803,
%U -1008411198,2640054791,-6911753175,18095204734,-47373861027,124026378347,-324705274014,850089443695,-2225563057071,5826599727518,-15254236125483
%N a(n) = 2(a(n-2) - a(n-1)) + a(n-3) where a(0)=-3, a(1)=11 & a(2)=-30.
%C Sequence relates bisections of Lucas and Fibonacci numbers.
%C Pisano period lengths: 1, 3, 4, 6, 5, 12, 8, 6, 12, 15, 10, 12, 7, 24, 20, 12, 9, 12, 18, 30, ... - _R. J. Mathar_, Aug 10 2012
%H Indranil Ghosh, <a href="/A098150/b098150.txt">Table of n, a(n) for n = 0..2383</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 (-3,-1).
%F 2*A098149(n) + a(n) = 8*(-1)^(n+1)*A001519(n) - (-1)^(n+1)*A005248(n+1).
%F a(n) = - 3a(n-1) - a(n-2). - _Tanya Khovanova_, Feb 02 2007
%F G.f.: (2x-3)/(1+3x+x^2). - _Philippe Deléham_, Nov 16 2008
%F a(n) = (-1)^(n+1)*(3*L(2n+1)-F(2n)), where F(n) is the n-th Fibonacci number and L(n) is the n-th Lucas number. - _Rigoberto Florez_, Dec 24 2018
%t a[0] = -3; a[1] = 11; a[2] = -30; a[n_] := a[n] = 2(a[n - 2] - a[n - 1]) + a[n - 3]; Table[ a[n], {n, 0, 25}] (* _Robert G. Wilson v_, Sep 04 2004 *)
%t RecurrenceTable[{a[0]==-3,a[1]==11,a[2]==-30,a[n]==2(a[n-2]-a[n-1])+ a[n-3]},a,{n,30}] (* or *) LinearRecurrence[{-3,-1},{-3,11},30] (* _Harvey P. Dale_, Feb 05 2012 *)
%t Table[(-1)^(n+1)(3LucasL[2n+1]-Fibonacci[2n]), {n,0,20}] (* _Rigoberto Florez_, Dec 24 2018 *)
%o (Magma) I:=[-3,11]; [n le 2 select I[n] else -3*Self(n-1)-Self(n-2): n in [1..35]]; // _Vincenzo Librandi_, Dec 26 2018
%Y Cf. A098149, A001519, A005248.
%K easy,sign
%O 0,1
%A _Creighton Dement_, Aug 29 2004
%E More terms from _Robert G. Wilson v_, Sep 04 2004
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