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A041684
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Numerators of continued fraction convergents to sqrt(362).
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2
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19, 723, 27493, 1045457, 39754859, 1511730099, 57485498621, 2185960677697, 83123991251107, 3160897628219763, 120197233863602101, 4570655784445099601, 173805117042777386939, 6609165103409985803283, 251322079046622237911693, 9556848168875055026447617
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OFFSET
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0,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (38,1).
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FORMULA
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From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 38*a(n-1) + a(n-2), n > 1; a(0)=19, a(1)=723.
G.f.: (19+x)/(1-38*x-x^2). (End)
a(n) = (1/2)*sqrt(362)*((19+sqrt(362))^n - (19-sqrt(362))^n) + (19/2)*((19-sqrt(362))^n + (19+sqrt(362))^n), with n >= 0. - Paolo P. Lava, Nov 28 2008
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MATHEMATICA
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Numerator[Convergents[Sqrt[362], 30]] (* Vincenzo Librandi, Nov 06 2013 *)
LinearRecurrence[{38, 1}, {19, 723}, 20] (* Harvey P. Dale, Feb 10 2019 *)
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CROSSREFS
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Cf. A041685.
Sequence in context: A078986 A180990 A041687 * A157165 A201708 A280625
Adjacent sequences: A041681 A041682 A041683 * A041685 A041686 A041687
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KEYWORD
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nonn,cofr,frac,easy
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Additional term from Colin Barker, Nov 09 2013
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STATUS
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approved
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