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Exponacci (or exponential Fibonacci) numbers.
3

%I #22 Oct 22 2024 20:48:23

%S 1,1,2,9,64,3125,1679616,96889010407,9223372036854775808,

%T 278128389443693511257285776231761,

%U 10000000000000000000000000000000000000000000000000000000

%N Exponacci (or exponential Fibonacci) numbers.

%H Alois P. Heinz, <a href="/A152915/b152915.txt">Table of n, a(n) for n = 0..15</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Fibonacci_number">Fibonacci number</a>

%F a(0) = 1, a(n) = n ^ Fibonacci(n) for n > 0; Fibonacci = A000045.

%e a(9) = 9 ^ Fibonacci(9) = 9 ^ 34 = 278128389443693511257285776231761.

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

%p seq(a(n), n=0..12); # _Alois P. Heinz_, Jun 17 2014

%t Array[ #^Fibonacci[ # ]&,12] (* _Vladimir Joseph Stephan Orlovsky_, Apr 03 2010 *)

%o (Other) unsigned long Exponacci(unsigned int n)

%o {

%o if (n == 0)

%o return 1;

%o return pow(n, Fibonacci(n));

%o }

%o (Magma) [n^Fibonacci(n): n in [1..10]]; // _Vincenzo Librandi_, Apr 05 2017

%Y Cf. A000045, A100399.

%Y Main diagonal of A244003.

%K nonn

%O 0,3

%A ShaoJun Ying (dolphinysj(AT)gmail.com), Dec 15 2008

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Apr 03 2010