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A042088
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Numerators of continued fraction convergents to sqrt(568).
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2
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23, 24, 119, 143, 6697, 6840, 34057, 40897, 1915319, 1956216, 9740183, 11696399, 547774537, 559470936, 2785658281, 3345129217, 156661602263, 160006731480, 796688528183, 956695259663, 44804670472681
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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 (0,0,0,286,0,0,0,-1).
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FORMULA
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G.f.: -(x^7 - 23*x^6 + 24*x^5 - 119*x^4 - 143*x^3 - 119*x^2 - 24*x - 23)/(x^8 - 286*x^4 + 1). - Vincenzo Librandi, Nov 16 2013
a(n) = 286*a(n-4) - a(n-8). - Vincenzo Librandi, Nov 16 2013
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MATHEMATICA
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Numerator[Convergents[Sqrt[568], 30]] (* or *) CoefficientList[Series[-(x^7 - 23 x^6 + 24 x^5 - 119 x^4 - 143 x^3 - 119 x^2 - 24 x - 23)/(x^8 - 286 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, 119, 143, 6697, 6840, 34057, 40897]; [n le 8 select I[n] else 286*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. A042089.
Sequence in context: A214510 A042084 A042082 * A042086 A042090 A042092
Adjacent sequences: A042085 A042086 A042087 * A042089 A042090 A042091
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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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