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A041160
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Numerators of continued fraction convergents to sqrt(90).
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2
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9, 19, 351, 721, 13329, 27379, 506151, 1039681, 19220409, 39480499, 729869391, 1499219281, 27715816449, 56930852179, 1052471155671, 2161873163521, 39966188099049, 82094249361619, 1517662676608191
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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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G.f.: (1 + x)*(9 + 10*x - x^2) / (1 - 38*x^2 + x^4). [Bruno Berselli, Oct 30 2013]
a(n) = (2+(-1)^n)*((3-sqrt(10))^(n+1)+(3+sqrt(10))^(n+1))/2. [Bruno Berselli, Oct 30 2013]
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MATHEMATICA
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Table[(2 + (-1)^n) ((3 - Sqrt[10])^(n + 1) + (3 + Sqrt[10])^(n + 1))/2, {n, 0, 30}] (* Bruno Berselli, Oct 30 2013 *)
LinearRecurrence[{0, 38, 0, -1}, {9, 19, 351, 721}, 30] (* Harvey P. Dale, May 12 2018 *)
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CROSSREFS
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KEYWORD
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nonn,cofr,frac,easy
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AUTHOR
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STATUS
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approved
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