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A101361
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a(1) = a(2) = 1; for n > 2, a(n) = Knuth's Fibonacci (or circle) product "a(n-1) o a(n-2)".
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0
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1, 1, 3, 8, 55, 987, 121393, 267914296, 72723460248141, 43566776258854844738105, 7084593923980518516849609894969925639, 690168906931029935139391829792095612517948949963798093315456
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| D. E. Knuth, Fibonacci multiplication, Appl. Math. Lett. 1 (1988), 57-60.
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FORMULA
| a(n) = Fib(2*Fib(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). [From T. D. Noe (noe(AT)sspectra.com), Mar 17 2009]
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EXAMPLE
| 1o1 = 3, 1o3 = 8, 3o8 = 55, ...
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MAPLE
| with(combinat); f:=n->fibonacci(2*fibonacci(n));
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MATHEMATICA
| Table[ Fibonacci[2Fibonacci[n]], {n, 12}] (from Robert G. Wilson v Feb 12 2005)
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PROG
| (PARI) a(n)=if(n<1, 0, fibonacci(2*fibonacci(n)))
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CROSSREFS
| Cf. A101330.
Sequence in context: A026088 A192647 A121567 * A104034 A000825 A132517
Adjacent sequences: A101358 A101359 A101360 * A101362 A101363 A101364
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 26 2005
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EXTENSIONS
| Formula and more terms from Michael Somos, Feb 03, 2005.
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