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A041785
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Denominators of continued fraction convergents to sqrt(413).
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2
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1, 3, 28, 31, 152, 183, 1799, 5580, 224999, 680577, 6350192, 7030769, 34473268, 41504037, 408009601, 1265532840, 51029323201, 154353502443, 1440210845188, 1594564347631, 7818468235712, 9413032583343, 92535761485799, 287020317040740, 11573348443115399
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OFFSET
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0,2
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 226798, 0, 0, 0, 0, 0, 0, 0, -1).
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FORMULA
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G.f.: -(x^14 -3*x^13 +28*x^12 -31*x^11 +152*x^10 -183*x^9 +1799*x^8 -5580*x^7 -1799*x^6 -183*x^5 -152*x^4 -31*x^3 -28*x^2 -3*x -1) / (x^16 -226798*x^8 +1). - Colin Barker, Nov 24 2013
a(n) = 226798*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 24 2013
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MATHEMATICA
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Denominator[Convergents[Sqrt[413], 30]] (* Vincenzo Librandi, Dec 24 2013 *)
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PROG
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(Magma) I:=[1, 3, 28, 31, 152, 183, 1799, 5580, 224999, 680577, 6350192, 7030769, 34473268, 41504037, 408009601, 1265532840]; [n le 16 select I[n] else 226798*Self(n-8)-Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 24 2013
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CROSSREFS
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Cf. A041784, A040392.
Sequence in context: A224579 A037102 A042169 * A157848 A225674 A253653
Adjacent sequences: A041782 A041783 A041784 * A041786 A041787 A041788
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KEYWORD
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nonn,frac,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Colin Barker, Nov 24 2013
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STATUS
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approved
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