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A101361 a(1) = a(2) = 1; for n > 2, a(n) = Knuth's Fibonacci (or circle) product "a(n-1) o a(n-2)". 2
1, 1, 3, 8, 55, 987, 121393, 267914296, 72723460248141, 43566776258854844738105, 7084593923980518516849609894969925639, 690168906931029935139391829792095612517948949963798093315456 (list; graph; refs; listen; history; text; internal format)
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: A192647 A121567 A222788 * A104034 A000825 A273433

Adjacent sequences:  A101358 A101359 A101360 * A101362 A101363 A101364

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jan 26 2005

EXTENSIONS

Formula and more terms from Michael Somos, Feb 03 2005

STATUS

approved

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Last modified July 19 22:14 EDT 2019. Contains 325168 sequences. (Running on oeis4.)