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A097691
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Denominators of the continued fraction n-1/(n-1/...) [n times].
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7
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1, 2, 8, 56, 551, 6930, 105937, 1905632, 39424240, 922080050, 24057287759, 692686638072, 21817946138353, 746243766783074, 27543862067299424, 1091228270370045824, 46187969968474139807, 2080128468827570457762, 99318726126650358502921, 5011361251329169946919800
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OFFSET
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1,2
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COMMENTS
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The (n-1)-th term of the Lucas sequence U(n,1). The numerator is the n-th term. Adjacent terms of the sequence U(n,1) are relatively prime.
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LINKS
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FORMULA
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a(n) = abs((2^(-n) * (sqrt(4 - n^2) + i*n)^n - 2^n*(-sqrt(4 - n^2) - i*n)^(-n))/sqrt(4 - n^2)), where i is the imaginary unit, for n > 2. - Daniel Suteu, May 31 2017
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EXAMPLE
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a(4) = 56 because 4-1/(4-1/(4-1/4)) = 209/56.
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MATHEMATICA
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Table[s=n; Do[s=n-1/s, {n-1}]; Denominator[s], {n, 20}]
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PROG
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(Sage) [lucas_number1(n, n, 1) for n in range(1, 19)] # Zerinvary Lajos, Jul 16 2008
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CROSSREFS
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KEYWORD
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easy,frac,nonn
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AUTHOR
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STATUS
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approved
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