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A228778
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a(n) = 2^Fibonacci(n) + 1.
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0
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2, 3, 3, 5, 9, 33, 257, 8193, 2097153, 17179869185, 36028797018963969, 618970019642690137449562113, 22300745198530623141535718272648361505980417, 13803492693581127574869511724554050904902217944340773110325048447598593
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n+2) = a(n+1)*a(n) - a(n) - a(n+1) + 2, a(0)=2, a(1)=3.
Binet type formula: log_2(a(n)-1) = (1/sqrt(5)) * (r^n - s^n), where r and s are the roots of x^2-x-1. (this is true by definition).
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MAPLE
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a:= n-> 1 + 2^(<<0|1>, <1|1>>^n)[1, 2]:
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MATHEMATICA
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Table[2^Fibonacci[n] + 1, {n, 0, 13}] (* T. D. Noe, Sep 07 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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