A101361 - OEIS (original) (raw)

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

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)):

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)))

EXTENSIONS

Formula and more terms from Michael Somos, Feb 03 2005