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A206419 Fibonacci sequence beginning 11, 7.

%I A206419 #19 Sep 08 2022 08:46:01
%S A206419 11,7,18,25,43,68,111,179,290,469,759,1228,1987,3215,5202,8417,13619,
%T A206419 22036,35655,57691,93346,151037,244383,395420,639803,1035223,1675026,
%U A206419 2710249,4385275,7095524,11480799,18576323,30057122,48633445,78690567,127324012
%N A206419 Fibonacci sequence beginning 11, 7.
%H A206419 Vincenzo Librandi, <a href="/A206419/b206419.txt">Table of n, a(n) for n = 1..1000</a>
%H A206419 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1).
%F A206419 From _Andrew Howroyd_, Aug 28 2018: (Start)
%F A206419 a(n) = a(n-1) + a(n-2) for n > 2.
%F A206419 a(n) = 11*Fibonacci(n) - 4*Fibonacci(n-1).
%F A206419 G.f.: x*(11 - 4*x)/(1 - x - x^2).
%F A206419 (End)
%t A206419 LinearRecurrence[{1, 1}, {11, 7}, 60]
%t A206419 CoefficientList[Series[x (11-4x)/(1-x-x^2),{x,0,40}],x] (* _Harvey P. Dale_, Jun 24 2021 *)
%o A206419 (Magma) I:=[11, 7]; [n le 2 select I[n] else Self(n-1)+Self(n-2): n in [1..50]]; // _Vincenzo Librandi_, Feb 18 2012
%o A206419 (PARI) Vec((11 - 4*x)/(1 - x - x^2) + O(x^30)) \\ _Andrew Howroyd_, Aug 28 2018
%Y A206419 Cf. A000045.
%K A206419 nonn
%O A206419 1,1
%A A206419 _Vladimir Joseph Stephan Orlovsky_, Feb 07 2012