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A041171
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Denominators of continued fraction convergents to sqrt(95).
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2
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1, 1, 3, 4, 75, 79, 233, 312, 5849, 6161, 18171, 24332, 456147, 480479, 1417105, 1897584, 35573617, 37471201, 110516019, 147987220, 2774285979, 2922273199, 8618832377, 11541105576, 216358732745, 227899838321, 672158409387, 900058247708, 16873206868131, 17773265115839
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OFFSET
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0,3
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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 (0,0,0,78,0,0,0,-1).
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FORMULA
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G.f.: (1 +x +3*x^2 +4*x^3 -3*x^4 +x^5 -x^6)/(1 -78*x^4 +x^8). - Vincenzo Librandi, Dec 12 2013
a(n) = 78*a(n-4) - a(n-8). - Vincenzo Librandi, Dec 12 2013
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MATHEMATICA
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Denominator[Convergents[Sqrt[95], 30]] (* or *) CoefficientList[Series[(1 + x + 3 x^2 + 4 x^3 - 3 x^4 + x^5 - x^6)/(1 - 78 x^4 + x^8), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 12 2013 *)
LinearRecurrence[{0, 0, 0, 78, 0, 0, 0, -1}, {1, 1, 3, 4, 75, 79, 233, 312}, 30] (* Harvey P. Dale, Mar 12 2016 *)
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PROG
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(Magma) I:=[1, 1, 3, 4, 75, 79, 233, 312]; [n le 8 select I[n] else 78*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
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CROSSREFS
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Cf. A041170.
Sequence in context: A318208 A341851 A132414 * A279935 A111799 A135237
Adjacent sequences: A041168 A041169 A041170 * A041172 A041173 A041174
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KEYWORD
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nonn,frac,easy
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Vincenzo Librandi, Dec 12 2013
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STATUS
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approved
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