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A042381
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Denominators of continued fraction convergents to sqrt(717).
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2
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1, 1, 4, 9, 112, 121, 2048, 2169, 28076, 58321, 203039, 261360, 13793759, 14055119, 55959116, 125973351, 1567639328, 1693612679, 28665442192, 30359054871, 392974100644, 816307256159, 2841895869121, 3658203125280, 193068458383681, 196726661508961
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13996798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
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FORMULA
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G.f.: -(x^22 -x^21 +4*x^20 -9*x^19 +112*x^18 -121*x^17 +2048*x^16 -2169*x^15 +28076*x^14 -58321*x^13 +203039* x^12 -261360*x^11 -203039*x^10 -58321*x^9 -28076*x^8 -2169*x^7 -2048*x^6 -121*x^5 -112*x^4 -9*x^3 -4*x^2 -x -1)/(x^24 -13996798*x^12 +1). - Vincenzo Librandi, Jan 21 2014
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MATHEMATICA
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Denominator[Convergents[Sqrt[717], 30]] (* Harvey P. Dale, Feb 12 2013 *)
CoefficientList[Series[-(x^22 - x^21 + 4 x^20 - 9 x^19 + 112 x^18 - 121 x^17 + 2048 x^16 -2169 x^15 + 28076 x^14 - 58321 x^13 + 203039 x^12 - 261360 x^11 - 203039 x^10 - 58321 x^9 - 28076 x^8 - 2169 x^7 - 2048 x^6 - 121 x^5 - 112 x^4 - 9 x^3 - 4 x^2 - x - 1)/(x^24 - 13996798 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 21 2014 *)
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PROG
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(Magma) I:=[1, 1, 4, 9, 112, 121, 2048, 2169, 28076, 58321, 203039, 261360, 13793759, 14055119, 55959116, 125973351, 1567639328, 1693612679, 28665442192, 30359054871, 392974100644, 816307256159, 2841895869121, 3658203125280]; [n le 24 select I[n] else 13996798*Self(n-12)-Self(n-24): n in [1..30]]; // Vincenzo Librandi, Jan 21 2014
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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