A101361 a(1) = a(2) = 1; for n > 2, a(n) = Knuth's Fibonacci (or circle) product "a(n-1) o a(n-2)".

1, 1, 3, 8, 55, 987, 121393, 267914296, 72723460248141, 43566776258854844738105, 7084593923980518516849609894969925639, 690168906931029935139391829792095612517948949963798093315456

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..17

D. E. Knuth, Fibonacci multiplication, Appl. Math. Lett. 1 (1988), 57-60.

Formula

a(n) = Fibonacci(2*Fibonacci(n)).

Third-order nonlinear recursion: a(0)=1, a(1)=1, a(2)=3, a(n)=(a(n-1)^2 - a(n-2)^2)/a(n-3). - T. D. Noe, Mar 17 2009

Example

1o1 = 3, 1o3 = 8, 3o8 = 55, ...

Maple

with(combinat); f:=n->fibonacci(2*fibonacci(n));
# second Maple program:
F:= n-> (<<0|1>, <1|1>>^n)[1, 2]:
a:= n-> F(2*F(n)):
seq(a(n), n=1..12);  # Alois P. Heinz, Jan 20 2017

Mathematica

Table[ Fibonacci[2Fibonacci[n]], {n, 12}] (* Robert G. Wilson v, Feb 12 2005 *)

Prog

(PARI) a(n)=if(n<1, 0, fibonacci(2*fibonacci(n)))

Crossrefs

Cf. A000045, A101330.

Sequence in context: A121567 A222788 A308572 * A104034 A000825 A273433

Adjacent sequences: A101358 A101359 A101360 * A101362 A101363 A101364

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 26 2005

Extensions

Formula and more terms from Michael Somos, Feb 03 2005

Status

approved