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A000301
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a(n) = a(n-1)*a(n-2) with a(0) = 1, a(1) = 2; also a(n) = 2^Fibonacci(n).
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40
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1, 2, 2, 4, 8, 32, 256, 8192, 2097152, 17179869184, 36028797018963968, 618970019642690137449562112, 22300745198530623141535718272648361505980416, 13803492693581127574869511724554050904902217944340773110325048447598592
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Continued fraction expansion of s = A073115 = 1.709803442861291... = Sum_{k >= 0} (1/2^floor(k * phi)) where phi is the golden ratio (1 + sqrt(5))/2. - Benoit Cloitre, Aug 19 2002
The continued fraction expansion of the above constant s is [1; 1, 2, 2, 4, ...], that of the rabbit constant r = s-1 = A014565 is [0; 1, 2, 2, 4, ...]. - M. F. Hasler, Nov 10 2018
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REFERENCES
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Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002, p. 913.
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LINKS
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FORMULA
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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
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A000301 := proc(n) option remember;
if n < 2 then 1+n
fi
end:
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MATHEMATICA
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PROG
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(Haskell)
a000301 = a000079 . a000045
a000301_list = 1 : scanl (*) 2 a000301_list
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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