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A041693
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Denominators of continued fraction convergents to sqrt(366).
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2
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1, 7, 8, 15, 23, 61, 755, 1571, 2326, 3897, 6223, 47458, 1809627, 12714847, 14524474, 27239321, 41763795, 110766911, 1370966727, 2852700365, 4223667092, 7076367457, 11300034549, 86176609300, 3286011187949, 23088254924943, 26374266112892, 49462521037835
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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, 0, 0, 0, 0, 1815850, 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 -7*x^21 +8*x^20 -15*x^19 +23*x^18 -61*x^17 +755*x^16 -1571*x^15 +2326*x^14 -3897*x^13 +6223*x^12 -47458*x^11 -6223*x^10 -3897*x^9 -2326*x^8 -1571*x^7 -755*x^6 -61*x^5 -23*x^4 -15*x^3 -8*x^2 -7*x-1)/(x^24 -1815850*x^12 +1). - Vincenzo Librandi, Dec 23 2013
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MATHEMATICA
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Denominator[Convergents[Sqrt[366], 30]] (* or *) CoefficientList[Series[-(x^22 - 7 x^21 + 8 x^20 - 15 x^19 + 23 x^18 - 61 x^17 + 755 x^16 - 1571 x^15 + 2326 x^14 - 3897 x^13 + 6223 x^12 - 47458 x^11 - 6223 x^10 - 3897 x^9 - 2326 x^8 - 1571 x^7 - 755 x^6 - 61 x^5 - 23 x^4 - 15 x^3 - 8 x^2 - 7 x - 1)/(x^24 - 1815850 x^12 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 23 2013 *)
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PROG
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(Magma) I:=[1, 7, 8, 15, 23, 61, 755, 1571, 2326, 3897, 6223, 47458, 1809627, 12714847, 14524474, 27239321, 41763795, 110766911, 1370966727, 2852700365, 4223667092, 7076367457, 11300034549, 86176609300]; [n le 24 select I[n] else 1815850*Self(n-12)-Self(n-24): n in [1..40]]; // Vincenzo Librandi, Dec 23 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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