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A022092 Fibonacci sequence beginning 0, 9.

%I A022092 #23 Apr 10 2025 06:52:22
%S A022092 0,9,9,18,27,45,72,117,189,306,495,801,1296,2097,3393,5490,8883,14373,
%T A022092 23256,37629,60885,98514,159399,257913,417312,675225,1092537,1767762,
%U A022092 2860299,4628061,7488360,12116421,19604781,31721202,51325983,83047185,134373168
%N A022092 Fibonacci sequence beginning 0, 9.
%D A022092 A. T. Benjamin and J. J. Quinn, Proofs that really count: the art of combinatorial proof, M.A.A. 2003, p. 15.
%H A022092 G. C. Greubel, <a href="/A022092/b022092.txt">Table of n, a(n) for n = 0..1000</a>
%H A022092 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A022092 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,1).
%F A022092 a(n) = 9*Fibonacci(n).
%F A022092 a(n) = F(n+4) + F(n+1) + F(n-2) + F(n-4), n>3, where F = A000045.
%F A022092 a(n) = round((18*phi-9)/5 phi^n), for n > 4. - _Thomas Baruchel_, Sep 08 2004
%F A022092 G.f.: 9*x/(1-x-x^2). - _Philippe Deléham_, Nov 20 2008
%t A022092 9*Fibonacci[Range[0,40]] (* _Vladimir Joseph Stephan Orlovsky_, Sep 17 2008 *)
%o A022092 (Magma)
%o A022092 A022092:= func< n | 9*Fibonacci(n) >;
%o A022092 [A022092(n): n in [0..40]]; // _G. C. Greubel_, Apr 10 2025
%o A022092 (SageMath)
%o A022092 def A022092(n): return 9*fibonacci(n)
%o A022092 print([A022092(n) for n in range(41)]) # _G. C. Greubel_, Apr 10 2025
%Y A022092 Cf. A000032, A000045.
%Y A022092 Sequences of the form m*Fibonacci listed in A022086.
%K A022092 nonn,easy
%O A022092 0,2
%A A022092 _N. J. A. Sloane_