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A041389
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Denominators of continued fraction convergents to sqrt(209).
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2
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1, 2, 11, 35, 81, 278, 1471, 3220, 91631, 186482, 1024041, 3258605, 7541251, 25882358, 136953041, 299788440, 8531029361, 17361847162, 95340265171, 303382642675, 702105550521, 2409699294238, 12750602021711, 27910903337660, 794255895476191, 1616422694290042
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OFFSET
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0,2
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,93102,0,0,0,0,0,0,0,-1).
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FORMULA
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G.f.: -(x^14 -2*x^13 +11*x^12 -35*x^11 +81*x^10 -278*x^9 +1471*x^8 -3220*x^7 -1471*x^6 -278*x^5 -81*x^4 -35*x^3 -11*x^2 -2*x -1) / (x^16 -93102*x^8 +1). - Colin Barker, Nov 16 2013
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MATHEMATICA
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Denominator[Convergents[Sqrt[209], 30]] (* Harvey P. Dale, Nov 07 2012 *)
CoefficientList[Series[-(x^14 - 2 x^13 + 11 x^12 - 35 x^11 + 81 x^10 - 278 x^9 + 1471 x^8 - 3220 x^7 - 1471 x^6 - 278 x^5 - 81 x^4 - 35 x^3 - 11 x^2 - 2 x - 1)/(x^16 - 93102 x^8 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 17 2013 *)
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PROG
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(Magma) I:=[1, 2, 11, 35, 81, 278, 1471, 3220, 91631, 186482, 1024041, 3258605, 7541251, 25882358, 136953041, 299788440]; [n le 16 select I[n] else 93102*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 17 2013
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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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