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%I #33 Sep 08 2022 08:45:48
%S 1,3,11,30,79,207,542,1419,3715,9726,25463,66663,174526,456915,
%T 1196219,3131742,8199007,21465279,56196830,147125211,385178803,
%U 1008411198,2640054791,6911753175,18095204734,47373861027,124026378347,324705274014,850089443695
%N a(n)=3*a(n-1)-a(n-2) with a(0)=1, a(1)=3, a(2)=11.
%H Harvey P. Dale, <a href="/A167375/b167375.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 (3, -1).
%F a(n) = (-1)^n*A098150(n-1), n>0.
%F G.f.: (3*x^2+1)/(1-3*x+x^2).
%F a(n) = 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 Join[{1},LinearRecurrence[{3,-1},{3,11},30]] (* _Harvey P. Dale_, Jun 25 2014 *)
%t CoefficientList[Series[(3 x^2 + 1)/(1 - 3 x + x^2), {x, 0, 40}], x] (* _Vincenzo Librandi_, Jun 26 2014 *)
%t Table[3LucasL[2n+1]-Fibonacci[2n], {n,0,20}] (* _Rigoberto Florez_, Dec 24 2018 *)
%o (Magma) I:=[1,3,11]; [n le 3 select I[n] else 3*Self(n-1)-Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Jun 26 2014
%Y Cf. A135929, A138034.
%K nonn,easy
%O 0,2
%A _Jamel Ghanouchi_, Nov 02 2009
%E Edited by _R. J. Mathar_, Nov 03 2009
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