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A000301
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a(n) = a(n-1)*a(n-2); also a(n) = 2^Fibonacci(n).
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16
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1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, 36028797018963968, 618970019642690137449562112, 22300745198530623141535718272648361505980416, 13803492693581127574869511724554050904902217944340773110325048447598592
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Continued fraction expansion of s=1.709803442861291...=sum( k>=0,1/2^floor(k*PHI) ) where PHI is the golden ratio (1+sqrt(5))/2 - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 19 2002
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REFERENCES
| J. L. Davison, A series and its associated continued fraction, Proc. Amer. Math. Soc., 63 (1977), 29-32.
Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002, p. 913.
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LINKS
| S. Giraudo, Intervals of balanced binary trees in the Tamari lattice, arXiv preprint arXiv:1107.3472 (2011).
Index to divisibility sequences
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FORMULA
| a(n) ~ k^phi^n with k = 2^(1/sqrt(5)) = 1.3634044 and phi the golden ratio. [Charles R Greathouse IV, Jan 12 2012]
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MAPLE
| A000301 := proc(n) option remember; if n <=2 then n else A000301(n-1)*A000301(n-2); fi; end;
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MATHEMATICA
| Table[f=Fibonacci[n]; 2^f, {n, 0, 12}] (Vladimir Orlovsky, Jul 21 2008)
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PROG
| (MAGMA) [2^Fibonacci(n): n in [0..20]]; // Vincenzo Librandi, Apr 18 2011
(PARI) a(n)=1<<fibonacci(n) \\ Charles R Greathouse IV, Jan 12 2012
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CROSSREFS
| Sequence in context: A070323 A109213 A109214 * A124439 A082836 A201376
Adjacent sequences: A000298 A000299 A000300 * A000302 A000303 A000304
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Offset changed from 1 to 0 by Vincenzo Librandi, Apr 18 2011
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