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A206420 Fibonacci sequence beginning 11, 8.

%I A206420 #29 Mar 17 2025 15:55:38
%S A206420 11,8,19,27,46,73,119,192,311,503,814,1317,2131,3448,5579,9027,14606,
%T A206420 23633,38239,61872,100111,161983,262094,424077,686171,1110248,1796419,
%U A206420 2906667,4703086,7609753,12312839,19922592,32235431,52158023,84393454,136551477
%N A206420 Fibonacci sequence beginning 11, 8.
%H A206420 Vincenzo Librandi, <a href="/A206420/b206420.txt">Table of n, a(n) for n = 1..1000</a>
%H A206420 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A206420 From _Andrew Howroyd_, Aug 28 2018: (Start)
%F A206420 a(n) = a(n-1) + a(n-2) for n > 2.
%F A206420 a(n) = 11*Fibonacci(n) - 3*Fibonacci(n-1).
%F A206420 G.f.: x*(11 - 3*x)/(1 - x - x^2). (End)
%t A206420 LinearRecurrence[{1, 1}, {11, 8}, 60]
%o A206420 (Magma) I:=[11, 8]; [n le 2 select I[n] else Self(n-1)+ Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Feb 18 2012
%o A206420 (PARI) Vec((11 - 3*x)/(1 - x - x^2) + O(x^30)) \\ _Andrew Howroyd_, Aug 28 2018
%o A206420 (Python)
%o A206420 def aupton(terms):
%o A206420     alst = [11, 8]
%o A206420     for n in range(3, terms+1):
%o A206420         alst.append(alst[-1] + alst[-2])
%o A206420     return alst[:terms]
%o A206420 print(aupton(36)) # _Michael S. Branicky_, Nov 08 2021
%Y A206420 Cf. A000045.
%K A206420 nonn,easy
%O A206420 1,1
%A A206420 _Vladimir Joseph Stephan Orlovsky_, Feb 07 2012