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A022091 Fibonacci sequence beginning 0, 8.

%I A022091 #33 Apr 16 2025 09:56:36
%S A022091 0,8,8,16,24,40,64,104,168,272,440,712,1152,1864,3016,4880,7896,12776,
%T A022091 20672,33448,54120,87568,141688,229256,370944,600200,971144,1571344,
%U A022091 2542488,4113832,6656320,10770152,17426472,28196624,45623096,73819720,119442816
%N A022091 Fibonacci sequence beginning 0, 8.
%D A022091 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.
%H A022091 G. C. Greubel, <a href="/A022091/b022091.txt">Table of n, a(n) for n = 0..1000</a>
%H A022091 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022091 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A022091 a(n) = round( (16phi-8)/5 phi^n) (works for n>4). - _Thomas Baruchel_, Sep 08 2004
%F A022091 a(n) = 8*F(n) = F(n+4) + F(n) + F(n-4) for n>3, where F=A000045.
%F A022091 G.f.: 8*x/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008
%t A022091 8*Fibonacci[Range[0,41]] (* _Vladimir Joseph Stephan Orlovsky_, Sep 17 2008; modified by _G. C. Greubel_, Apr 13 2025 *)
%t A022091 LinearRecurrence[{1,1},{0,8},40] (* _Harvey P. Dale_, Jan 19 2018 *)
%o A022091 (Magma)
%o A022091 A022091:= func< n | 8*Fibonacci(n) >;
%o A022091 [A022091(n): n in [0..40]]; // _G. C. Greubel_, Apr 13 2025
%o A022091 (SageMath)
%o A022091 def A022091(n): return 8*fibonacci(n)
%o A022091 print([A022091(n) for n in range(41)]) # _G. C. Greubel_, Apr 13 2025
%Y A022091 Cf. A000032, A000045, A258160.
%Y A022091 Sequences of the form m*Fibonacci are listed in A022086.
%K A022091 nonn,easy
%O A022091 0,2
%A A022091 _N. J. A. Sloane_