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A042098
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Numerators of continued fraction convergents to sqrt(573).
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2
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23, 24, 359, 383, 17977, 18360, 275017, 293377, 13770359, 14063736, 210662663, 224726399, 10548077017, 10772803416, 161367324841, 172140128257, 8079813224663, 8251953352920, 123607160165543
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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
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 766, 0, 0, 0, -1).
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FORMULA
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G.f.: -(x^7 - 23*x^6 + 24*x^5 - 359*x^4 - 383*x^3 - 359*x^2 - 24*x - 23)/(x^8 - 766*x^4 + 1). - Vincenzo Librandi, Nov 16 2013
a(n) = 766*a(n-4) - a(n-8). Vincenzo Librandi, Nov 16 2013
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MATHEMATICA
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Numerator[Convergents[Sqrt[573], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 359 x^4 - 383 x^3 - 359 x^2 - 24 x - 23)/(x^8 - 766 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 16 2013 *)
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PROG
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(MAGMA) I:=[23, 24, 359, 383, 17977, 18360, 275017, 293377]; [n le 8 select I[n] else 766*Self(n-4)-Self(n-8): n in [1..30]]; // Vincenzo Librandi, Nov 16 2013
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CROSSREFS
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Cf. A042099.
Sequence in context: A042092 A042094 A042096 * A041263 A042100 A042101
Adjacent sequences: A042095 A042096 A042097 * A042099 A042100 A042101
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KEYWORD
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nonn,cofr,frac,easy,less
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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