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 A007570 a(n) = F(F(n)), where F is a Fibonacci number. (Formerly M1537) 21

%I M1537

%S 0,1,1,1,2,5,21,233,10946,5702887,139583862445,1779979416004714189,

%T 555565404224292694404015791808,

%U 2211236406303914545699412969744873993387956988653,2746979206949941983182302875628764119171817307595766156998135811615145905740557

%N a(n) = F(F(n)), where F is a Fibonacci number.

%C Asymptotic behavior as n->infinity: a(n+1)=a(n)*phi^(F(n-1)), with phi = A001622 = 1.61803... (golden ratio). - _Carmine Suriano_, Jan 24 2011

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe and Alois P. Heinz, <a href="/A007570/b007570.txt">Table of n, a(n) for n = 0..19</a> (terms n = 0..17 from T. D. Noe)

%H E. A. Parberry, Two recursion relations for F(F(n)), Fib. Quart., 15 (1977), <a href="http://www.fq.math.ca/Scanned/15-2/parberry-a.pdf">122</a> and <a href="http://www.fq.math.ca/Scanned/15-2/parberry-b.pdf">139</a>.

%H C. Street, <a href="http://www.codehappy.net/fibo.pdf">A Recurrence for the Sequence {F(F(n)),n=>0}</a>

%p F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:

%p a:= n-> F(F(n)):

%p seq(a(n), n=0..14); # _Alois P. Heinz_, Oct 09 2015

%t F[0] = 0; F[1] = 1; F[n_] := F[n] = F[n - 1] + F[n - 2]; Table[ F[ F[n] ], {n, 0, 14} ]

%t Fibonacci[Fibonacci[Range[0,20]]] (* _Harvey P. Dale_, May 05 2012 *)

%o (Sage) [fibonacci(fibonacci(n)) for n in xrange(0, 14)] # _Zerinvary Lajos_, Nov 30 2009

%o (PARI) a(n)=fibonacci(fibonacci(n)) \\ _Charles R Greathouse IV_, Feb 03 2014

%Y Cf. A000045, A005371, A058051.

%K nonn,nice,easy

%O 0,5

%A _N. J. A. Sloane_, _Robert G. Wilson v_

%E One more term from _Harvey P. Dale_, May 05 2012

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Last modified February 21 18:45 EST 2019. Contains 320376 sequences. (Running on oeis4.)