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A267319
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Continued fraction expansion of phi^8, where phi = (1 + sqrt(5))/2.
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0
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46, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1, 45, 1
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OFFSET
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0,1
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COMMENTS
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More generally, the ordinary generating function for the continued fraction expansion of phi^(2*k + 1), where phi = (1 + sqrt(5))/2), k = 1, 2, 3,... is floor(phi^(2*k + 1))/(1 - x), and for the continued fraction expansion of phi^(2*k) is (floor(phi^(2*k)) + x - x^2)/(1 - x^2).
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LINKS
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FORMULA
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G.f.: (46 + x - x^2)/(1 - x^2).
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EXAMPLE
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phi^8 = (47 + 21*sqrt(5))/2 = 46 + 1/(1 + 1/(45 + 1/(1 + 1/(45 + 1/(1 + 1/(45 + 1/...)))))).
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MATHEMATICA
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ContinuedFraction[(47 + 21 Sqrt[5])/2, 82]
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PROG
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CROSSREFS
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KEYWORD
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nonn,cofr,easy
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AUTHOR
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STATUS
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approved
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