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A005370 a(n) = Fibonacci(Fibonacci(n+1) + 1).

%I A005370 M0891 #38 Nov 15 2022 02:41:39
%S A005370 1,1,2,3,8,34,377,17711,9227465,225851433717,2880067194370816120,
%T A005370 898923707008479989274290850145,
%U A005370 3577855662560905981638959513147239988861837901112,4444705723234237498833973519982908519933430818636409166351397897095281987215864
%N A005370 a(n) = Fibonacci(Fibonacci(n+1) + 1).
%D A005370 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005370 Alois P. Heinz, <a href="/A005370/b005370.txt">Table of n, a(n) for n = 0..18</a>
%p A005370 with(combinat, fibonacci): A005370 := n -> fibonacci(fibonacci(n+1)+1);
%p A005370 # second Maple program:
%p A005370 F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
%p A005370 a:= n-> F(F(n+1)+1):
%p A005370 seq(a(n), n=1..14);  # _Alois P. Heinz_, Nov 05 2015
%t A005370 Table[Fibonacci[Fibonacci[n+1] +1], {n, 0, 14}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 08 2012 *)
%o A005370 (Magma) [Fibonacci(Fibonacci(n+1)+1): n in [0..17]]; // _Vincenzo Librandi_, Apr 20 2011
%o A005370 (SageMath) [fibonacci(fibonacci(n+1) +1) for n in range(15)] # _G. C. Greubel_, Nov 14 2022
%Y A005370 Cf. A000045, A007570.
%K A005370 nonn
%O A005370 0,3
%A A005370 _N. J. A. Sloane_
%E A005370 More terms from _David W. Wilson_
%E A005370 Description corrected by Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Nov 17 2002