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A042075
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Denominators of continued fraction convergents to sqrt(561).
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2
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1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040, 1077398196369, 1100476017409
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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, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
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FORMULA
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G.f.: -(x^26 -x^25 +3*x^24 -16*x^23 +19*x^22 -35*x^21 +89*x^20 -213*x^19 +515*x^18 -728*x^17 +1243*x^16 -6943*x^15 +15129*x^14 -22072*x^13 -15129*x^12 -6943*x^11 -1243*x^10 -728*x^9 -515*x^8 -213*x^7 -89*x^6 -35*x^5 -19*x^4 -16*x^3 -3*x^2 -x -1)/(x^28 -1045570*x^14 +1). - Vincenzo Librandi, Jan 14 2014
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MATHEMATICA
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Denominator[Convergents[Sqrt[561], 30]] (* or *) CoefficientList[Series[-(x^26 - x^25 + 3 x^24 - 16 x^23 + 19 x^22 - 35 x^21 + 89 x^20 - 213 x^19 + 515 x^18 - 728 x^17 + 1243 x^16 - 6943 x^15 + 15129 x^14 - 22072 x^13 - 15129 x^12 - 6943 x^11 - 1243 x^10 - 728 x^9 - 515 x^8 - 213 x^7 - 89 x^6 - 35 x^5 - 19 x^4 - 16 x^3 - 3 x^2 - x - 1)/(x^28 - 1045570 x^14 + 1), {x, 0, 40}], x] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1045570, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 16, 19, 35, 89, 213, 515, 728, 1243, 6943, 15129, 22072, 1030441, 1052513, 3135467, 16729848, 19865315, 36595163, 93055641, 222706445, 538468531, 761174976, 1299643507, 7259392511, 15818428529, 23077821040}, 30] (* Harvey P. Dale, Mar 01 2015 *)
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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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